C₁₁×#8305 #14585498

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8304
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#8305

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂³×D₄×C₁₁	C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

1154 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 182 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) = 39
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1293);