C₁₁×#11970 #14589163

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11970

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

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

normal subgroups only

This group has 284 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)(12,13,15,19,16,18,24,26)(14,20,21,27,22,17,23,25)(28,29,33,39,34,37,49,55,35,40,47,57,31,46,32,38)(30,41,44,54,42,56,43,51,45,58,48,36,50,52,59,53);(12,14,16,22)(13,17,18,20)(15,23,24,21)(19,27,26,25)(28,30)(29,36)(31,42)(32,48)(33,43)(34,50)(35,45)(37,51)(38,56)(39,41)(40,54)(44,49)(46,53)(47,59)(52,55)(57,58);(13,18)(17,20)(19,26)(25,27)(28,31,35,34)(29,37,40,46)(30,42,45,50)(32,47,49,33)(36,51,54,53)(38,39,55,57)(41,52,58,56)(43,48,59,44)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4958);