C₁₁×#7078 #14584271

order	2816
nilpotency class	4
isoclinism	isoclinic class of #7076
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7078

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#327
commutator	C₂²×C₈	C₂×C₄×C₁₁
Frattini, cosocle	C₂×C₂²⋊C₈	C₂²×C₁₁
prime radical	C₂⁴×C₁₁	D₈
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×C₂²⋊C₈ ◁ G

286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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 — 2 generators on 35 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 66);