C₁₁×#11895 #14589088

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11895

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

442 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 118 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)(14,18,19,16)(15,17)(20,21,24,29,26,31,25,30)(22,27,32,28,23,34,33,35);(12,14)(13,16)(15,19)(17,18)(21,27)(22,32)(23,33)(24,25)(28,30)(29,35)(31,34);(14,19)(16,18)(20,22,25,33,26,23,24,32)(21,28,29,34,31,35,30,27)

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, 4883);