C₁₁×#7832 #14585025

order	2816
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#7832

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

322 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 59
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)(28,29,32,35)(30,33,37,40)(31,34,38,41)(36,42,43,39)(44,45,48,52)(46,49,54,58)(47,50,55,51)(53,56,59,57);(12,14,17,23)(13,18,20,27)(15,22,16,25)(19,26,24,21)(28,30)(29,33)(31,36)(32,37)(34,39)(35,40)(38,43)(41,42)(44,46,48,54)(45,49,52,58)(47,53,55,59)(50,56,51,57);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(28,31)(29,34)(30,36)(32,38)(33,39)(35,41)(37,43)(40,42)(45,50)(47,55)(49,56)(51,52)(53,59)(57,58)

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, 820);