C₁₁×#7116 #14584309

order	2816
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7116

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#329
commutator	C₄²	C₂×C₈×C₁₁
Frattini, cosocle	C₂×#97	C₂²×C₁₁
prime radical	C₂×C₁₁×#127	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

282 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 352

A minimal faithful permutation representation — 2 generators on 35 points:

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

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, 104);