C₁₁×#11543 #14588736

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11543

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₁
prime radical	C₂⁵×C₁₁	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁴×C₁₁ ◁ C₂²×C₁₁×C₂²⋊C₄ ◁ G

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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)(12,13,15,20,16,21,27,35)(14,22,24,34,23,36,37,43)(17,19,26,32,28,33,39,42)(18,29,31,38,30,40,41,25);(12,14,17,25)(13,18,19,22)(15,24,26,29)(16,23,28,38)(20,34,32,31)(21,30,33,36)(27,37,39,40)(35,43,42,41);(14,23)(18,30)(22,36)(24,37)(25,38)(29,40)(31,41)(34,43)

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4531);