C₁₁×#13078 #14590271

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13078

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

454 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 146 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)(12,13,17,24,19,23,18,42)(14,25,29,55,28,52,40,56)(15,30,32,51,33,21,41,50)(16,34,37,44,39,66,38,22)(20,43,46,27,48,62,47,35)(26,54,59,74,58,71,60,75)(31,64,65,53,36,67,68,49)(45,70,72,61,63,69,73,57);(12,14,16,35,18,29,38,43,19,28,39,27,17,40,37,62)(13,20,44,25,24,47,66,56,23,48,22,52,42,46,34,55)(15,26,36,57,32,60,68,69,33,58,31,61,41,59,65,70)(21,45,49,54,51,72,67,74,30,63,53,71,50,73,64,75);(12,15)(13,21)(14,26)(16,36)(17,41)(18,32)(19,33)(20,45)(22,53)(23,30)(24,51)(25,54)(27,61)(28,58)(29,60)(31,39)(34,64)(35,57)(37,65)(38,68)(40,59)(42,50)(43,69)(44,49)(46,73)(47,72)(48,63)(52,71)(55,75)(56,74)(62,70)(66,67)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6066);