C₁₁×#32949 #14610142

order	2816
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₁×#32949

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₁₁×#585	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

1278 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 290 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 — 4 generators on 75 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,23)(14,24,29,47)(15,20,32,42)(16,21,34,44)(17,35,25,22)(19,36,39,28)(26,45,52,67)(27,46,54,68)(30,55,57,40)(31,58,48,41)(33,59,49,43)(37,60,63,51)(38,61,64,53)(50,70,72,66)(56,65,69,74)(62,71,73,75);(12,14,25,36,18,29,17,28)(13,19,35,47,23,39,22,24)(15,26,48,60,32,52,31,51)(16,27,49,61,34,54,33,53)(20,37,58,67,42,63,41,45)(21,38,59,68,44,64,43,46)(30,50,69,75,57,72,56,71)(40,62,74,70,55,73,65,66);(12,15)(13,20)(14,26)(16,30)(17,31)(18,32)(19,37)(21,40)(22,41)(23,42)(24,45)(25,48)(27,50)(28,51)(29,52)(33,56)(34,57)(35,58)(36,60)(38,62)(39,63)(43,65)(44,55)(46,66)(47,67)(49,69)(53,71)(54,72)(59,74)(61,75)(64,73)(68,70);(12,16)(13,21)(14,27)(15,30)(17,33)(18,34)(19,38)(20,40)(22,43)(23,44)(24,46)(25,49)(26,50)(28,53)(29,54)(31,56)(32,57)(35,59)(36,61)(37,62)(39,64)(41,65)(42,55)(45,66)(47,68)(48,69)(51,71)(52,72)(58,74)(60,75)(63,73)(67,70)

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, 25937);