Finite Group Databasebeta

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C3×C5×C373⋊C3 #30680933

order16785
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C373⋊C3
unambiguous semidirect productC373⋊(C32×C5)
unambiguous semidirect product(C3×C373)⋊(C3×C5)
unambiguous semidirect product(C5×C373)⋊C32
unambiguous semidirect product(C3×C5×C373)⋊C3

Splittings

Fitting, socleC3×C5×C373 ⋊ C3
derived, SylowC373 ⋊ C32×C5
HallC5×C373 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C5C373⋊C3
commutator, cosocle, hypocenterC373C32×C5
FrattiniC1G
Fitting, socleC3×C5×C373C3
LCSG ▷ C373
UCSC1 ◁ C3×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5595

Conjugacy classes & character table

1905 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D373⋊C3, C3×C5⋊(D373⋊C3), C3×D5×C373⋊C3, …
maximal normal subgroup ofC3×C5×D373⋊C3, C3×C5⋊(D373⋊C3), C3×D5×C373⋊C3, …
maximal quotient ofC2×C3×C5×C373⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16785, 4);