C₁₁×#11989 #14589182

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11989
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11989

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1551
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#3176	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#405 ◁ G

292 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 98 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)(12,13,15,21,16,20,28,36,17,22,29,37,30,18,27,31)(14,23,25,38,26,19,32,33,24,35,39,43,40,34,41,42);(13,18)(15,27)(16,30)(19,23)(20,22)(21,37)(25,41)(26,40)(28,29)(32,39)(33,42)(34,35);(12,14)(13,19,22,34)(15,25)(16,26)(17,24)(18,23,20,35)(21,33,37,42)(27,41)(28,32)(29,39)(30,40)(31,38,36,43)

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, 4977);