C₁₁×#10689 #14587882

order	2816
nilpotency class	3
isoclinism	isoclinic class of #10370
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#10689

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	#400
prime radical	C₂³×C₁₁	C₂²⋊Q₈
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

248 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 98 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)(12,13,15,16)(14,17,19,18)(20,21,24,23,25,27,29,33)(22,28,30,35,31,32,34,26);(12,14,15,19)(13,17,16,18)(20,22,29,30,25,31,24,34)(21,26,33,28,27,35,23,32);(13,16)(14,18)(17,19)(20,23,24,27,25,33,29,21)(22,28,30,35,31,32,34,26)

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, 3677);