C₁₁×#12297 #14589490

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

Aliases

direct product

C₁₁×#12297

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₁₁×#466	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₁₁×#424 ◁ G

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

normal subgroups only

This group has 290 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)(28,29)(30,42)(31,45)(32,48)(33,40)(34,39)(35,41)(36,43)(37,47)(38,51)(44,56)(46,55)(49,58)(50,53)(52,57)(54,59);(12,14)(13,17)(15,20)(16,21)(18,23)(19,24)(22,27)(25,26)(28,30,35,31)(29,36,41,55)(32,49,52,59)(33,44,34,47)(37,53,56,38)(39,54,40,58)(42,57,45,48)(43,50,46,51);(12,15,16,22)(13,18,19,25)(14,20,21,27)(17,23,24,26)(28,31,35,30)(29,37,41,56)(32,46,52,43)(33,44,34,47)(36,53,55,38)(39,42,40,45)(48,54,57,58)(49,51,59,50)

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, 5285);