C₁₁×#12464 #14589657

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12463
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12464

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1675
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#135	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

172 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 74 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)(12,13,19,25)(14,26,32,58)(15,33)(16,38,40,23)(17,22,27,53)(18,42,39,24)(20,43,47,29)(21,48)(28,61)(30,56,59,46)(31,45,66,57)(34,52)(35,69)(36,54)(37,49)(41,50)(44,63)(51,60)(55,70)(62,68)(64,72)(65,71)(67,74)(73,75);(12,14,27,59,18,31,16,29,19,32,17,30,39,66,40,43)(13,20,23,45,24,46,22,26,25,47,38,57,42,56,53,58)(15,28,60,75,35,63,34,62,37,65,41,67,36,64,48,70)(21,44,54,73,50,61,49,55,52,72,69,74,51,71,33,68);(12,15)(13,21)(14,28)(16,34)(17,41)(18,35)(19,37)(20,44)(22,49)(23,54)(24,50)(25,52)(26,55)(27,60)(29,62)(30,67)(31,63)(32,65)(33,53)(36,39)(38,69)(40,48)(42,51)(43,70)(45,73)(46,61)(47,72)(56,71)(57,74)(58,68)(59,75)(64,66)

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5452);