C₁₁×#9394 #14586587

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9383
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#9394

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

506 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 154 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) = 704

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

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

Conjugacy classes & character table

539 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2382);