C₂³×SD₁₆×C₂₃ #15671194

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂³×SD₁₆×C₂₃

	subgroup	G/H
center, socle	C₂⁴×C₂₃	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

1720 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 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);(7,8,9,10,11,12,13,14);(8,10)(9,13)(12,14)

1288 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2307);