Finite Group Databasebeta

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C3×C5×#11725133 #27210523

order13260
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×#11725133

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC13×C17 ⋊ C3×C4×C5
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ Dic13
HallC3×C5×C13 ⋊ #595
HallC5×C17 ⋊ C3×Dic13
HallC5×C13 ⋊ C3×#595
HallC3×C17 ⋊ C5×Dic13
HallC3×C13 ⋊ C5×#595
SylowC17 ⋊ C3×C5×Dic13
SylowC13 ⋊ C3×C5×#595

Subgroups

subgroupG/H
center, hypercenterC3×C5#11725133
commutator, hypocenterC13×C17C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C5×C13×D17C2
cosocleC13×D17C2×C3×C5
LCSG ▷ C13×C17
UCSC1 ◁ C3×C5

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

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 73);