C₁₁×#7817 #14585010

order	2816
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7817

Subgroups

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

410 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 2816

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

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 805);