Finite Group Databasebeta

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C3×C5×D113⋊C7 #37557543

order23730
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D113⋊C7
unambiguous semidirect productD113⋊(C3×C5×C7)
unambiguous semidirect product(C3×D113)⋊(C5×C7)
unambiguous semidirect product(C113⋊C7)⋊(C2×C3×C5)
unambiguous semidirect product(C5×D113)⋊(C3×C7)
unambiguous semidirect product(C3×C5×D113)⋊C7

Splittings

Fitting, socle, HallC3×C5×C113 ⋊ C2×C7
derived, SylowC113 ⋊ C2×C3×C5×C7
HallC3×C5×C113⋊C7 ⋊ C2
HallC5×C113⋊C7 ⋊ C2×C3
HallC3×C5×D113 ⋊ C7
HallC3×C113⋊C7 ⋊ C2×C5
HallC5×D113 ⋊ C3×C7
HallC113⋊C7 ⋊ C2×C3×C5
HallC3×D113 ⋊ C5×C7
HallC5×C113 ⋊ C2×C3×C7
HallC3×C113 ⋊ C2×C5×C7
HallD113 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5D113⋊C7
commutator, cosocle, hypocenterC113C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C113C2×C7
LCSG ▷ C113
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 19);