Finite Group Databasebeta

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C3×C5×D373⋊C3 #46777064

order33570
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×D373⋊C3
unambiguous semidirect productD373⋊(C32×C5)
unambiguous semidirect product(C373⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C3×D373)⋊(C3×C5)
unambiguous semidirect product(C5×D373)⋊C32
unambiguous semidirect product(C3×C5×D373)⋊C3

Splittings

Fitting, socleC3×C5×C373 ⋊ C2×C3
derived, SylowC373 ⋊ C2×C32×C5
HallC3×C5×C373⋊C3 ⋊ C2
HallC5×D373 ⋊ C32
HallC3×C373⋊C3 ⋊ C2×C5
HallC5×C373 ⋊ C2×C32
HallD373 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5D373⋊C3
commutator, cosocle, hypocenterC373C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C373C2×C3
LCSG ▷ C373
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5595

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(33570, 14);