C₁₁×#12296 #14589489

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

Aliases

direct product

C₁₁×#12296

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#424 ◁ G

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

normal subgroups only

This group has 278 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) = 1408

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

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, 5284);