C₁₁×#11892 #14589085

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11855
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#11892

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

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

normal subgroups only

This group has 396 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) = 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)(20,21,25,31,27,33,26,32)(22,34,37,44,39,49,38,48)(23,40,24,43,42,30,41,29)(28,35,45,36,47,51,46,50);(12,14)(13,16)(15,19)(17,18)(20,22,27,39)(21,28,33,47)(23,36,42,50)(24,35,41,51)(25,38,26,37)(29,34,43,49)(30,44,40,48)(31,46,32,45);(14,19)(16,18)(20,23,26,41,27,42,25,24)(21,29,31,40,33,43,32,30)(22,35,38,50,39,51,37,36)(28,44,45,49,47,48,46,34)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4880);