C₁₁×#7144 #14584337

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#7144

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#95
commutator	C₂×C₄	C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₁
socle	C₂²×C₁₁	#336
prime radical	C₂³×C₁₁	C₂²⋊C₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

210 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 2 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20,22,26)(15,18)(16,19)(17,21,24,27)(23,25)(28,29,31,35,32,37,42,49,33,36,43,48,44,50,55,58)(30,38,40,51,41,52,54,59,39,34,45,46,53,47,56,57);(12,14)(13,17,19,24)(15,21)(16,22)(18,20,25,26)(23,27)(28,30)(29,34,36,38)(31,40)(32,41)(33,39)(35,46,48,51)(37,47,50,52)(42,54)(43,45)(44,53)(49,57,58,59)(55,56)

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, 132);