C₁₁×#11838 #14589031

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#11838

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1514
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×M₁₆ ◁ G

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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)(14,23)(15,27,29,37)(16,19)(17,22)(18,24,34,42)(20,31,38,41)(21,30)(25,39)(26,40)(28,33,43,35)(32,36);(12,14,17,26)(13,18,22,34)(15,28,29,43)(16,32,30,25)(19,33,21,35)(20,36,38,39)(23,27,40,37)(24,41,42,31);(13,19,22,21)(15,29)(18,33,34,35)(20,37,38,27)(23,39,40,36)(24,42)(28,43)(31,41)

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4826);