C₁₁×#21828 #14599021

order	2816
nilpotency class	3
isoclinism	isoclinic class of #17405
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₁×#21828

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂⁴×C₁₁	C₂⁴
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₁₁×C₄⋊C₄ ◁ G

990 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 366 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) = 704

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 14816);