C₁₁×#8514 #14585707

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#8514

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#379
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#3568	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

648 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 138 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)(12,13,16,23,19,14,25,29)(15,31,34,67,36,57,53,66)(17,39,37,49,42,65,54,60)(18,24,38,21,43,30,55,27)(20,44,46,71,26,56,45,33)(22,50,52,62,28,61,64,41)(32,68,35,51,70,75,72,63)(40,47,73,48,74,58,69,59);(12,14)(13,19)(15,26)(16,21)(17,39)(18,30)(20,36)(22,41)(23,38)(24,43)(25,27)(28,62)(29,55)(31,40)(32,45)(33,51)(34,48)(35,58)(37,64)(42,65)(44,66)(46,70)(47,72)(49,61)(50,60)(52,54)(53,59)(56,67)(57,74)(63,71)(68,73)(69,75);(12,15)(13,20)(14,26)(16,34)(17,40)(18,35)(19,36)(21,48)(22,51)(23,46)(24,47)(25,53)(27,59)(28,63)(29,45)(30,58)(31,39)(32,55)(33,41)(37,73)(38,70)(42,74)(43,72)(44,50)(49,67)(52,75)(54,69)(56,61)(57,65)(60,66)(62,71)(64,68)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1502);