C₂²×C₅×C₇×C₉×C₁₉ #37560917

order	23940
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₅×C₇×C₉×C₁₉
multiplicative	(ℤ/24257)ˣ, (ℤ/25631)ˣ, (ℤ/35913)ˣ, (ℤ/47884)ˣ, (ℤ/48514)ˣ, (ℤ/51262)ˣ, (ℤ/71826)ˣ

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 23940

A minimal faithful permutation representation — 2 generators on 44 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);(3,4)

23940 conjugacy classes. The character table is too large to display.

automorphism group of	C₁₂₇×C₁₉₁
outer automorphism group of	C₁₂₇×C₁₉₁

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 49);