C₁₁×#14673 #14591866

order	2816
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

direct product

C₁₁×#14673

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂⁶×C₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ G

2734 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 7661);