C₂⁴×Q₈×C₂₃ #15671208

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₂₃ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂⁴×Q₈×C₂₃

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₂₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁶×C₂₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₂₃ ◁ G

6264 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 6 generators on 39 points:

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

1840 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2321);