C₂²×#41×C₂₃ #13092131

order	1472
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂²×#41×C₂₃

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

890 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 5 generators on 35 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1472, 263);