C₁₁×#10380 #14587573

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10378
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#10380

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#393
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

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

normal subgroups only

This group has 390 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) = 35
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 35 points:

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

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, 3368);