C₁₁×#7089 #14584282

order	2816
nilpotency class	4
isoclinism	isoclinic class of #7076
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#7089

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#327
commutator	C₂²×C₈	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₄⋊C₈	C₂²×C₁₁
prime radical	C₂³×C₁₁	#102
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

180 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 704

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 77);