C₁₁×#11552 #14588745

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11549
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#11552

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

366 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 3 generators on 43 points:

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4540);