C₁₁×#11967 #14589160

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11855
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11967

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

290 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 122 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)(28,29,32,37,33,38,47,55,34,39,48,56,46,54,31,36)(30,40,42,52,43,53,41,57,44,58,45,35,49,50,59,51);(12,14,16,22)(13,17,18,20)(15,23,24,21)(19,27,26,25)(28,30)(29,35)(31,45)(32,41)(33,49)(34,44)(36,53)(37,40)(38,57)(39,52)(42,47)(43,46)(48,59)(50,55)(51,54)(56,58);(13,18)(17,20)(19,26)(25,27)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4955);