C₁₁×#7411 #14584604

order	2816
nilpotency class	5
isoclinism	isoclinic class of #7410
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#7411

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1344
commutator	C₂²×C₈	C₂×C₄×C₁₁
Frattini, cosocle	#408	C₂²×C₁₁
prime radical	C₂×C₁₁×#41	D₄
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#408 ◁ G

162 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 43 points:

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

Conjugacy classes & character table

275 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 399);