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C13×D15×D17 #27210582

order13260
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D15×D17
unambiguous semidirect product(C3×D17)⋊(D5×C13)
unambiguous semidirect product(C5×D17)⋊(D3×C13)

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C22
derived, HallC3×C5×C17 ⋊ C22×C13
HallC5×C13×C17 ⋊ C2×D3
HallC3×C13×C17 ⋊ C2×D5
HallC13×C17 ⋊ C2×D15
HallC3×C5×C13 ⋊ C2×D17
HallC5×C17 ⋊ C2×D3×C13
HallC5×C13 ⋊ D3×D17
HallC3×C17 ⋊ C2×D5×C13
HallC3×C13 ⋊ D5×D17
SylowC17 ⋊ C2×C13×D15
HallC3×C5 ⋊ C2×C13×D17
SylowC5 ⋊ D3×C13×D17
SylowC3 ⋊ D5×C13×D17

Subgroups

subgroupG/H
center, hypercenterC13D15×D17
commutator, cosocle, hypocenterC3×C5×C17C22×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C17C22
LCSG ▷ C3×C5×C17
UCSC1 ◁ C13

80 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:

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

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 132);