Finite Group Databasebeta

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C5×C3⋊(D113⋊C7) #37557547

order23730
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(D113⋊C7)
unambiguous semidirect productC3⋊(C5×D113⋊C7)
unambiguous semidirect productD339⋊(C5×C7)
unambiguous semidirect product(C113⋊C7)⋊(C5×D3)
unambiguous semidirect product(C5×D339)⋊C7

Splittings

Fitting, socle, HallC3×C5×C113 ⋊ C2×C7
derived, HallC3×C113 ⋊ C2×C5×C7
HallC3×C5×C113⋊C7 ⋊ C2
HallC5×C113⋊C7 ⋊ D3
HallC5×D339 ⋊ C7
HallC3×C113⋊C7 ⋊ C2×C5
HallC113⋊C7 ⋊ C5×D3
HallD339 ⋊ C5×C7
HallC5×C113 ⋊ D3×C7
SylowC113 ⋊ C5×D3×C7
HallC3×C5 ⋊ D113⋊C7
SylowC3 ⋊ C5×D113⋊C7

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(D113⋊C7)
commutator, cosocle, hypocenterC3×C113C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C113C2×C7
LCSG ▷ C3×C113
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1695

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 23);