C₁₁×#11458 #14588651

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11458

Subgroups

	subgroup	G/H
center	C₄×C₁₁	C₂×#99
commutator	C₂³	C₂²×C₈×C₁₁
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
socle	C₂×C₁₁	C₂×#324
prime radical	C₂⁴×C₁₁	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₁₁×M₁₆ ◁ G

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,20,16,21,26,34,17,19,25,31,27,32,38,41)(14,18,23,29,24,30,37,40,22,28,35,33,36,39,43,42);(12,14)(13,18,19,28)(15,23)(16,24)(17,22)(20,33,31,29)(21,30,32,39)(25,35)(26,37)(27,36)(34,42,41,40)(38,43);(14,22)(18,28)(23,35)(24,36)(29,33)(30,39)(37,43)(40,42)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4446);