Finite Group Databasebeta

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C3×C5×D313⋊C3 #43245239

order28170
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×D313⋊C3
unambiguous semidirect productD313⋊(C32×C5)
unambiguous semidirect product(C313⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C3×D313)⋊(C3×C5)
unambiguous semidirect product(C5×D313)⋊C32
unambiguous semidirect product(C3×C5×D313)⋊C3

Splittings

Fitting, socleC3×C5×C313 ⋊ C2×C3
derived, SylowC313 ⋊ C2×C32×C5
HallC3×C5×C313⋊C3 ⋊ C2
HallC5×D313 ⋊ C32
HallC3×C313⋊C3 ⋊ C2×C5
HallC5×C313 ⋊ C2×C32
HallD313 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5D313⋊C3
commutator, cosocle, hypocenterC313C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C313C2×C3
LCSG ▷ C313
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28170, 14);