C₁₁×#8141 #14585334

order	2816
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₁ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₁×#8141

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#376
prime radical	C₂³×C₁₁	#117
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

294 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 704

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

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1129);