C₁₃×#13663 #15700002

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13663

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂²×C₁₃×C₁₆ ◁ G

298 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 49
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 49 points:

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

Conjugacy classes & character table

637 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6651);