C₁₁×#12059 #14589252

order	2816
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12059

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×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×C₈×C₁₁ ◁ C₄×C₁₁×C₁₆ ◁ G

212 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 130 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)(14,20)(15,23)(16,18)(17,21)(19,25)(22,27)(24,26)(28,29,31,35,32,36,39,42,33,30,34,37,40,38,41,43);(12,14,16,22)(13,17,18,26)(15,24,25,21)(19,27,23,20);(13,18)(17,26)(19,23)(20,27)(28,30,31,37,32,38,39,43,33,29,34,35,40,36,41,42)

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5047);