C₁₁×#12397 #14589590

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12397

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂×D₄×C₁₁	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈×D₄×C₁₁ ◁ G

278 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 82 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)(12,13,17,21)(14,22,25,26)(15,20,16,19)(18,24,27,23)(28,29,34,38)(30,39,42,57)(31,36,33,48)(32,44,47,58)(35,50,53,41)(37,43,55,46)(40,56,49,54)(45,51,59,52);(12,14,17,25)(13,18,21,27)(15,24,16,23)(19,26,20,22)(28,30)(29,35)(31,40)(32,45)(33,49)(34,42)(36,51)(37,54)(38,53)(39,44)(41,46)(43,50)(47,59)(48,52)(55,56)(57,58);(13,19)(15,16)(18,26)(20,21)(22,27)(23,24)(28,31,34,33)(29,36,38,48)(30,40,42,49)(32,43,47,46)(35,51,53,52)(37,44,55,58)(39,56,57,54)(41,45,50,59)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5385);