C₁₁×#12385 #14589578

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

Aliases

direct product

C₁₁×#12385

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈×Q₈×C₁₁ ◁ G

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

normal subgroups only

This group has 300 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)(12,13,16,19)(14,20,21,27)(15,23,24,18)(17,25,26,22)(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);(15,24)(18,23)(20,27)(22,25)(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);(12,14,16,21)(13,17,19,26)(15,25,24,22)(18,27,23,20)(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, 5373);