C₁₃×#13661 #15700000

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13661

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

334 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 832

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)(18,19)(20,24)(21,33)(22,36)(23,28)(25,29)(26,30)(27,34)(31,43)(32,39)(35,49)(37,45)(38,44)(40,48)(41,46)(42,47);(19,24)(20,29)(21,30)(22,34)(25,26)(27,43)(28,39)(31,48)(32,46)(33,37)(35,47)(36,38)(40,49)(41,42)(44,45);(15,17)

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, 6649);