C₁₁×#7353 #14584546

order	2816
nilpotency class	5
isoclinism	isoclinic class of #1406
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#7353

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#353
commutator	C₄²	C₂×C₈×C₁₁
Frattini, cosocle	#382	C₂²×C₁₁
prime radical	C₂³×C₁₁	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#382 ◁ G

204 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 51
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15,17,18,19)(20,21)(22,30,32,45)(23,34,35,50)(24,37,39,28)(25,29)(26,31,40,47)(27,36)(33,43,38,46)(41,48,42,49)(44,51);(20,22,25,33)(21,26,29,42)(23,31,35,49)(24,38,39,32)(27,43,44,30)(28,40,37,41)(34,46,50,45)(36,47,51,48)

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, 341);