C₂²×C₂₃×#127 #15671059

order	2944
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂²×C₂₃×#127

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

3000 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1472

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);(6,8)(10,11);(9,10,12,11);(5,6,7,8)(9,11,12,10)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2172);