C₁₁×#9976 #14587169

order	2816
nilpotency class	3
isoclinism	isoclinic class of #9974
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#9976

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

716 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 102 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)(14,16)(15,17)(18,19)(20,21,26,30)(22,31,35,43)(23,36,40,46)(24,41,25,29)(27,34,44,33)(28,38,47,39)(32,49,50,42)(37,48,51,45);(16,19)(20,22)(21,27)(23,37)(24,34)(25,33)(26,35)(28,45)(29,43)(30,44)(31,41)(32,38)(36,42)(39,50)(40,51)(46,49)(47,48);(12,14)(13,16)(15,18)(17,19)(20,23,26,40)(21,28,30,47)(22,32,35,50)(24,38,25,39)(27,42,44,49)(29,46,41,36)(31,48,43,45)(33,37,34,51)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 2964);