C₁₁×#7308 #14584501

order	2816
nilpotency class	4
isoclinism	isoclinic class of #7307
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#7308

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#342
commutator	C₂²×C₄	C₄²×C₁₁
Frattini, cosocle	C₂³×Q₈	C₂²×C₁₁
prime radical	C₂⁴×C₁₁	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁴×C₁₁ ◁ C₂³×Q₈×C₁₁ ◁ G

518 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 352

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)(15,17)(16,19)(20,21,23,27,24,28,32,35)(22,26,29,34,30,25,31,33);(12,14)(13,16,17,18)(15,19)(21,25,28,26)(27,34,35,33)

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, 296);