C₂²×C₃×C₇×C₁₁×C₂₅ #37528226

order	23100
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₇×C₁₁×C₂₅
multiplicative	(ℤ/24173)ˣ, (ℤ/26957)ˣ, (ℤ/34653)ˣ, (ℤ/34659)ˣ, (ℤ/46204)ˣ, (ℤ/48346)ˣ, (ℤ/53914)ˣ, (ℤ/69306)ˣ, (ℤ/69318)ˣ

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 23100

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39)(40,41,42,43,44,45,46,47,48,49,50);(3,4)

23100 conjugacy classes. The character table is too large to display.

automorphism group of	C₂₃×C₁₀₅₁
outer automorphism group of	C₂₃×C₁₀₅₁

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 37);