C₁₁×#11496 #14588689

order	2816
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#11496

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

296 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 138 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)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)(28,29,33,39,35,38,47,55,34,40,46,56,32,48,31,37)(30,41,44,51,43,36,50,52,45,54,58,59,49,53,42,57);(12,14,16,22)(13,17,19,20)(15,21,23,27)(18,24,25,26)(28,30,34,45)(29,36,40,53)(31,42,47,50)(32,49,35,43)(33,44,46,58)(37,51,55,59)(38,54,48,41)(39,52,56,57);(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26)(28,31,32,46,34,47,35,33)(29,37,48,56,40,55,38,39)(30,42,49,58,45,50,43,44)(36,51,41,57,53,59,54,52)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4484);