C₁₁×#13306 #14590499

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13306

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂⁴×C₁₁	D₈
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

566 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 1408

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

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

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, 6294);