C₁₁×#21827 #14599020

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×#21827

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
prime radical	C₂⁵×C₁₁	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₁₁×C₂²⋊C₄ ◁ G

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 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) = 352

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

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

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, 14815);