C₁₁×#9004 #14586197

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×#9004

Subgroups

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

458 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 47
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 47 points:

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

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, 1992);