C₁₁×#11896 #14589089

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×#11896

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

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

normal subgroups only

This group has 390 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) = 51
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,19,16)(15,17)(20,21,24,30,26,32,25,31)(22,33,35,49,37,43,36,47)(23,38,40,29,42,48,41,28)(27,39,44,34,46,50,45,51);(12,14)(13,16)(15,19)(17,18)(20,22,26,37)(21,27,32,46)(23,39,42,50)(24,36,25,35)(28,47,29,49)(30,45,31,44)(33,38,43,48)(34,40,51,41);(14,19)(16,18)(20,23,24,40,26,42,25,41)(21,28,31,48,32,29,30,38)(22,34,35,50,37,51,36,39)(27,43,45,49,46,33,44,47)

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, 4884);