C₁₁×#7351 #14584544

order	2816
nilpotency class	5
isoclinism	isoclinic class of #7349
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#7351

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1317
commutator	C₂⁴	C₂×C₈×C₁₁
Frattini, cosocle	#407	C₂²×C₁₁
prime radical	C₂⁴×C₁₁	C₂×C₈
LCS	G ▷ C₂⁴ ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#407 ◁ G

178 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 43
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,20,16,21,27,35,17,19,26,33,29,34,40,42)(14,18,23,30,24,32,37,41,22,31,25,38,28,36,39,43);(12,14)(13,18,19,31)(15,25)(16,28)(17,22)(20,30,33,38)(21,36,34,32)(23,26)(24,29)(27,37)(35,43,42,41)(39,40)

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 339);