C₁₁×#12463 #14589656

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

Aliases

direct product

C₁₁×#12463

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

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, 5451);