C₂²×C₃×C₅²×C₇×C₁₁ #37528408

order	23100
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

abelian	C₂²×C₃×C₅²×C₇×C₁₁
multiplicative	(ℤ/23501)ˣ, (ℤ/25421)ˣ, (ℤ/25531)ˣ, (ℤ/47002)ˣ, (ℤ/50842)ˣ, (ℤ/51062)ˣ

320 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 23100

A minimal faithful permutation representation — 2 generators on 35 points:

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

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

automorphism group of	C₇₁×C₃₃₁
outer automorphism group of	C₇₁×C₃₃₁

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 219);