C₁₁×#11486 #14588679

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2127
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11486

Subgroups

	subgroup	G/H
center	C₄×C₁₁	C₂×#99
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
socle	C₂×C₁₁	#1459
prime radical	C₁₁×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

364 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 126 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)(12,13,17,23,19,24,31,43,18,25,35,36,16,22,27,42)(14,26,29,39,28,38,15,21,30,40,33,41,34,20,32,37);(12,14)(13,20)(15,31)(16,34)(17,29)(18,30)(19,28)(21,23)(22,40)(24,26)(25,38)(27,32)(33,35)(36,37)(39,42)(41,43);(12,15,19,33,18,32,16,29)(13,21,24,41,25,37,22,39)(14,27,28,17,30,31,34,35)(20,36,26,42,38,23,40,43)

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, 4474);