C₁₁×C₁₆×Q₁₆ #14589245

order	2816
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×C₁₆×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₁×C₁₆	D₄
commutator	C₄	C₂²×C₁₁×C₁₆
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle, prime radical	C₂²×C₁₁	C₈×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁×C₁₆ ◁ C₄×C₁₁×C₁₆ ◁ G

218 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 2816

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

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

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5040);