C₂×C₂₃×#465 #15670666

order	2944
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₂₃×#465

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

564 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 37 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1779);