C₁₁×#7398 #14584591

order	2816
nilpotency class	5
isoclinism	isoclinic class of #7398
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7398

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1343
commutator	C₂²×C₈	C₂×C₄×C₁₁
Frattini, cosocle	#408	C₂²×C₁₁
prime radical	C₁₁×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#408 ◁ G

258 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 43 points:

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

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, 386);