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C13⋊C3×#66775 #27210496

order13260
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×#66775
unambiguous semidirect product(C13×#66775)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C17 ⋊ C3×C4
HallC13×#66775 ⋊ C3
HallC5×C17×C13⋊C3 ⋊ C4
HallC17×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC13×C17 ⋊ C3×AGL(1,𝔽5)
HallC5×C13⋊C3 ⋊ #595
HallC5×C17 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×#595
SylowC17 ⋊ AGL(1,𝔽5)×C13⋊C3
SylowC13 ⋊ C3×#66775
SylowC5 ⋊ C13⋊C3×#595

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C13×C17C3×C4
prime radicalC13⋊C3×D85C2
cosocleC13×D85C2×C3
LCSG ▷ C5×C13×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1105

A minimal faithful permutation representation — 2 generators on 35 points:

(2,6,4,3)(5,13,9,8)(7,11,10,12)(14,15,17,16)(19,22,21,20)(24,25,27)(26,29,32)(28,31,30)(33,35,34);(1,2,5,10,6,11,15,17,13,8,14,16,12,3,7,9,4)(18,19,20,22,21)(23,24,26,25,28,32,29,33,35,27,30,34,31)

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 46);