C₁₁×#12175 #14589368

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12173
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12175

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1598
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₁₁×#2190	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

346 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 70 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)(14,24)(15,28)(16,20)(17,22)(18,23)(19,25)(21,31)(26,40)(27,41)(29,34)(30,39)(32,38)(33,37)(35,43)(36,42);(12,14)(13,19)(15,29)(16,26)(17,33)(18,27)(20,34)(21,37)(22,35)(23,36)(24,28)(25,31)(30,43)(32,42)(38,40)(39,41);(13,20,23,22)(15,30)(19,34,36,35)(21,28,38,39)(24,40,41,37)(25,42)(29,43)(31,32)

Conjugacy classes & character table

275 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5163);