C₁₁×#12684 #14589877

order	2816
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#12684

Subgroups

	subgroup	G/H
center	C₈×C₁₁	#120
commutator	C₂³	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂×C₁₁	#1779
prime radical	C₁₁×#585	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₁ ◁ C₂²×C₈×C₁₁ ◁ G

894 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 210 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)(12,13,16,21,17,22,31,41,18,23,32,42,33,43,54,64)(14,19,26,36,27,37,50,60,25,35,48,58,49,59,69,73)(15,20,29,39,30,40,53,63,28,38,51,61,52,62,70,74)(24,44,46,65,47,66,68,75,45,34,55,56,67,57,71,72);(12,14)(13,19)(15,24)(16,26)(17,27)(18,25)(20,34)(21,36)(22,37)(23,35)(28,45)(29,46)(30,47)(31,50)(32,48)(33,49)(38,44)(39,56)(40,57)(41,60)(42,58)(43,59)(51,55)(52,67)(53,68)(54,69)(61,65)(62,66)(63,72)(64,73)(70,71)(74,75);(12,15)(13,20)(14,24)(16,29)(17,30)(18,28)(19,34)(21,39)(22,40)(23,38)(25,45)(26,46)(27,47)(31,53)(32,51)(33,52)(35,44)(36,56)(37,57)(41,63)(42,61)(43,62)(48,55)(49,67)(50,68)(54,70)(58,65)(59,66)(60,72)(64,74)(69,71)(73,75)

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5672);