Finite Group Databasebeta

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C3×C5⋊(D113⋊C7) #37557545

order23730
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5⋊(D113⋊C7)
unambiguous semidirect productC5⋊(C3×D113⋊C7)
unambiguous semidirect product(C113⋊C7)⋊(C3×D5)
unambiguous semidirect productD565⋊(C3×C7)
unambiguous semidirect product(C3×D565)⋊C7

Splittings

Fitting, socle, HallC3×C5×C113 ⋊ C2×C7
derived, HallC5×C113 ⋊ C2×C3×C7
HallC3×C5×C113⋊C7 ⋊ C2
HallC5×C113⋊C7 ⋊ C2×C3
HallC3×D565 ⋊ C7
HallC3×C113⋊C7 ⋊ D5
HallD565 ⋊ C3×C7
HallC113⋊C7 ⋊ C3×D5
HallC3×C113 ⋊ C7×D5
SylowC113 ⋊ C3×C7×D5
HallC3×C5 ⋊ D113⋊C7
SylowC5 ⋊ C3×D113⋊C7

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(D113⋊C7)
commutator, cosocle, hypocenterC5×C113C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C113C2×C7
LCSG ▷ C5×C113
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1695

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 21);