C₁₁×#10389 #14587582

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10386
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10389

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

406 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 43
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 43 points:

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

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, 3377);