C₁₁×#12809 #14590002

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11521
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12809

Subgroups

	subgroup	G/H
center	C₄×C₁₁	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×#41	C₂³×C₁₁
socle	C₂×C₁₁	#1799
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

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

normal subgroups only

This group has 420 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)(12,13,17,21,18,23,15,29)(14,24,27,35,28,40,25,19)(16,22,30,36,31,20,32,37)(26,39,41,34,42,38,43,33);(12,14,15,25,18,28,17,27)(13,19,21,24,23,35,29,40)(16,26,30,41,31,42,32,43)(20,33,36,38,22,34,37,39);(13,20)(16,31)(19,33)(21,36)(22,23)(24,38)(26,42)(29,37)(30,32)(34,35)(39,40)(41,43)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5797);