C₂³×C₁₁×#124 #14639853

order	2816
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₁ · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

C₂³×C₁₁×#124

	subgroup	G/H
center, socle	C₂⁵×C₁₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
prime radical	C₂⁴×D₄×C₁₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₁ ◁ G

14334 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 6 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55648);