C₁₁×#12303 #14589496

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12301
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12303

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1613
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₁
prime radical	C₁₁×#3204	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×M₁₆ ◁ G

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

normal subgroups only

This group has 322 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)(12,13,16,32,17,22,33,21)(14,23,26,38,27,37,25,19)(15,28,30,20,31,18,29,35)(24,36,42,40,43,39,41,34);(13,18)(15,29)(16,33)(19,34)(20,32)(21,35)(22,28)(23,39)(24,41)(25,26)(30,31)(36,37)(38,40)(42,43);(12,14,17,27)(13,19,22,38)(15,24,31,43)(16,26,33,25)(18,34,28,40)(20,39,35,36)(21,37,32,23)(29,41,30,42)

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, 5291);