C₁₁×#13333 #14590526

order	2816
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#13333

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
prime radical	C₂×C₁₁×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

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

normal subgroups only

This group has 546 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) = 47
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 47 points:

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

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, 6321);