C₁₁×#11914 #14589107

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11914

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1530
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	#97	C₂³×C₁₁
prime radical	C₂³×C₁₁	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#405 ◁ G

272 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 75
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 75 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,22,17,23,37,53,18,24,36,54,39,21,48,50)(14,25,27,56,28,19,40,42,29,43,61,51,38,44,34,67)(15,30,32,62,33,47,65,52,31,49,35,69,63,20,45,46)(26,41,58,71,59,70,68,74,57,72,60,73,66,55,64,75);(12,14,18,29)(13,19,24,44)(15,26,31,57)(16,34,36,40)(17,38,39,28)(20,41,47,72)(21,43,23,25)(22,51,54,56)(27,37,61,48)(30,55,49,70)(32,64,35,68)(33,66,63,59)(42,50,67,53)(45,58,65,60)(46,74,52,75)(62,71,69,73);(12,15,18,31)(13,20)(14,26,29,57)(16,35,36,32)(17,33,39,63)(19,41)(21,49)(22,52)(23,30)(24,47)(25,55)(27,60,61,58)(28,59,38,66)(34,68,40,64)(37,45,48,65)(42,73)(43,70)(44,72)(46,54)(50,62)(51,75)(53,69)(56,74)(67,71)

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, 4902);