Finite Group Databasebeta

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C3×C13×#66775 #27210526

order13260
isoclinismisoclinic class of #66775
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×#66775

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC5×C17 ⋊ C3×C4×C13
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC3×C5×C17 ⋊ C4×C13
HallC13×C17 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ #595
HallC5×C13 ⋊ C3×#595
HallC3×C17 ⋊ C13×AGL(1,𝔽5)
SylowC17 ⋊ C3×C13×AGL(1,𝔽5)
HallC3×C5 ⋊ C13×#595
SylowC5 ⋊ C3×C13×#595

Subgroups

subgroupG/H
center, hypercenterC3×C13#66775
commutator, hypocenterC5×C17C3×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C13×D85C2
cosocleD85C2×C3×C13
LCSG ▷ C5×C17
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 3315

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 76);