C₁₁×#12400 #14589593

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#12400

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#3355	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₁₁×#436 ◁ G

286 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 78 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)(28,29,33,37)(30,38,40,57)(31,42,44,56)(32,47,45,36)(34,49,50,39)(35,52,54,46)(41,58,48,53)(43,55,59,51);(12,14,17,25)(13,18,21,27)(15,24,16,23)(19,26,20,22)(28,30,33,40)(29,34,37,50)(31,43,44,59)(32,48,45,41)(35,53,54,58)(36,55,47,51)(38,56,57,42)(39,52,49,46);(13,19)(15,16)(18,26)(20,21)(22,27)(23,24)(31,44)(35,54)(38,57)(39,49)(42,56)(43,59)(46,52)(53,58)

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, 5388);