C₁₁×#12284 #14589477

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12284

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#3199	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#408 ◁ G

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

normal subgroups only

This group has 338 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) = 59
transitive degree	μ_t(G) = 704

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

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

Conjugacy classes & character table

341 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5272);