C₂²×C₃×C₁₁²×C₁₃ #34038387

order	18876
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₁₁

Aliases

abelian	C₂²×C₃×C₁₁²×C₁₃
multiplicative	(ℤ/19757)ˣ, (ℤ/39514)ˣ

280 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 18876

A minimal faithful permutation representation — 2 generators on 42 points:

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

18876 conjugacy classes. The character table is too large to display.

automorphism group of	C₂₃×C₈₅₉
outer automorphism group of	C₂₃×C₈₅₉

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18876, 69);