C₁₁×#8505 #14585698

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#8505

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#120
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#379
prime radical	C₁₁×#3531	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

648 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 704

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,17,19,22)(18,26,27,25)(28,29)(30,38,41,34)(31,42,43,53)(32,37)(33,36)(35,44,50,46)(39,55)(40,52,45,49)(47,51)(48,57)(54,58)(56,59);(12,13)(14,18)(15,22)(16,19)(17,24)(20,25)(21,27)(23,26)(28,30)(29,34)(31,39)(32,45)(33,41)(35,48)(36,38)(37,52)(40,47)(42,55)(43,56)(44,58)(46,57)(49,51)(50,54)(53,59);(12,14,16,21)(13,18,19,27)(15,23,24,20)(17,25,22,26)(28,31)(29,35)(30,39)(32,46)(33,43)(34,48)(36,50)(37,53)(38,54)(40,58)(41,56)(42,51)(44,47)(45,57)(49,55)(52,59)

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, 1493);