C₁₁×#13075 #14590268

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13075

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

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

normal subgroups only

This group has 458 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)(14,24)(15,30,32,20)(16,34)(17,39)(18,22)(19,27)(21,37)(23,36)(25,47)(26,48,55,68)(28,51)(29,61)(31,64,35,66)(33,45,65,63)(38,40)(41,54,62,57)(42,52)(43,59)(44,53,46,67)(49,60)(50,58)(56,74,73,70)(69,75,71,72);(12,14,25,52,17,29,16,27,18,28,37,60,36,58,38,59)(13,19,40,61,23,42,21,24,22,43,34,50,39,49,47,51)(15,26,53,72,33,56,35,57,32,55,67,75,65,73,31,54)(20,41,66,74,45,69,46,48,30,62,64,70,63,71,44,68);(12,15)(13,20)(14,26)(16,35)(17,33)(18,32)(19,41)(21,46)(22,30)(23,45)(24,48)(25,53)(27,57)(28,55)(29,56)(31,38)(34,64)(36,65)(37,67)(39,63)(40,66)(42,69)(43,62)(44,47)(49,71)(50,70)(51,68)(52,72)(54,59)(58,73)(60,75)(61,74)

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, 6063);