C₁₁×#12034 #14589227

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#12034

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	#107
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

204 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 118 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)(12,13,15,18,16,19,22,25)(14,17,21,24,20,23,26,27)(28,29)(30,39)(31,36)(32,46)(33,48)(34,38)(35,42)(37,40)(41,52)(43,58)(44,54)(45,51)(47,59)(49,56)(50,57)(53,55);(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27)(28,30,40,55,33,43,47,57,34,44,45,56,31,41,32,42)(29,35,46,52,36,49,51,54,38,50,59,58,48,53,37,39);(14,20)(17,23)(21,26)(24,27)(28,31,34,33)(29,36,38,48)(30,41,44,43)(32,45,47,40)(35,49,50,53)(37,46,51,59)(39,52,54,58)(42,56,57,55)

Conjugacy classes & character table

638 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5022);