C₁₁×#11953 #14589146

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11704
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11953

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

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

normal subgroups only

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4941);