C₁₁×#10983 #14588176

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8304
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₁×#10983

Subgroups

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

1318 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 286 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) = 35
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 35 points:

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

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, 3971);