C₁₁×#9068 #14586261

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9068

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#386
prime radical	C₂³×C₁₁	#123
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 404 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) = 1408

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2056);