C₁₁×#9005 #14586198

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#9005

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#386
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 416 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)(12,13,16,21,17,19,15,20)(14,22,25,18,24,27,23,26)(28,29)(30,39,42,50)(31,43)(32,37)(33,47)(34,38)(35,41,51,46)(36,44)(40,55,58,49)(45,52)(48,53)(54,56,59,57);(12,14)(13,18)(15,25)(16,23)(17,24)(19,26)(20,27)(21,22)(28,30,32,46,34,42,33,41)(29,35,37,50,38,51,47,39)(31,40,44,57,45,58,48,56)(36,49,52,59,53,55,43,54);(13,19)(15,16)(18,26)(23,25)(28,31)(29,36)(30,40)(32,44)(33,48)(34,45)(35,49)(37,52)(38,53)(39,54)(41,56)(42,58)(43,47)(46,57)(50,59)(51,55)

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, 1993);