C₁₁×#9496 #14586689

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₁×#9496

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#386
commutator	C₂⁴	C₂²×C₄×C₁₁
Frattini, cosocle	C₂⁵	C₂³×C₁₁
prime radical	C₂³×D₄×C₁₁	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁵×C₁₁ ◁ G

900 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 122 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 — 3 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)(22,25,29,32)(23,26)(24,27)(28,31,34,35)(30,33);(12,13)(14,16)(15,17)(18,19)(20,22)(21,25,27,32)(23,28)(24,29)(26,31,33,35)(30,34);(12,14)(13,16)(15,19)(17,18)(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,31,32,35)

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, 2484);