C₂²×C₃²×C₇²×C₁₃ #37524840

order	22932
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃×C₇

Aliases

abelian	C₂²×C₃²×C₇²×C₁₃
multiplicative	(ℤ/23521)ˣ, (ℤ/26803)ˣ, (ℤ/47042)ˣ, (ℤ/53606)ˣ

600 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 22932

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2)(5,6,7)(11,12,13,14,15,16,17)(25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4)(8,9,10)(18,19,20,21,22,23,24)

22932 conjugacy classes. The character table is too large to display.

automorphism group of	C₄₃×C₅₄₇
outer automorphism group of	C₄₃×C₅₄₇

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 785);