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GroupTheory

 Monster

 Calling Sequence Monster()

Description

 • The Fischer-Griess Monster $𝕄$ is the largest among the sporadic finite simple groups, discovered in 1973 by Robert Griess, after its existence had been predicted earlier by Griess and Bernd Fischer.  The Monster was constructed as the automorphism group of a certain $196883$-dimensional non-associative algebra.
 • The Monster() command returns a symbolic group that represents the Monster simple group.  Although the Monster is too large (about $1000000000000000000000000000$ times larger than the age of the universe in nanoseconds) to allow computation with its elements in the current implementation, Maple knows various properties of the group.
 • In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Monster}\left(\right)$
 ${G}{≔}{𝕄}$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${808017424794512875886459904961710757005754368000000000}$ (2)
 > $\mathrm{IsSimple}\left(G\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsPerfect}\left(G\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsSoluble}\left(G\right)$
 ${\mathrm{false}}$ (5)

Compatibility

 • The GroupTheory[Monster] command was introduced in Maple 17.