C₁₁×#10084 #14587277

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#10084

Subgroups

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

484 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 114 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)(16,17,22,27)(18,28,19,30)(20,26,21,25)(23,31,24,29)(32,33,37,35)(34,40,43,47)(36,44,46,39)(38,45,41,42);(12,13)(14,15)(16,18)(17,23)(19,22)(20,31)(21,29)(24,27)(25,30)(26,28)(32,34,37,43)(33,38,35,41)(36,45,46,42)(39,47,44,40);(13,15)(16,19,22,18)(17,24,27,23)(20,31,21,29)(25,30,26,28)(32,35,37,33)(34,41,43,38)(36,39,46,44)(40,45,47,42)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 3072);