C₂³×C₁₁×#127 #14639857

order	2816
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₁ · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂³×C₁₁×#127

	subgroup	G/H
center, socle	C₂⁵×C₁₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₁ ◁ G

24030 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 6 generators on 25 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25);(3,4);(5,6);(8,10)(12,13);(11,12,14,13);(7,8,9,10)(11,13,14,12)

1232 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55652);