Finite Group Databasebeta

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C7×D1035 #28408024

order14490
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1035
unambiguous semidirect productC5⋊(C7×D207)
unambiguous semidirect productC9⋊(C7×D115)
unambiguous semidirect productC23⋊(C7×D45)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C2
derived, HallC5×C9×C23 ⋊ C2×C7
HallC7×C9×C23 ⋊ D5
HallC5×C7×C23 ⋊ D9
HallC5×C7×C9 ⋊ D23
HallC9×C23 ⋊ C7×D5
HallC7×C23 ⋊ D45
HallC5×C23 ⋊ C7×D9
HallC7×C9 ⋊ D115
HallC5×C9 ⋊ C7×D23
HallC5×C7 ⋊ D207
SylowC23 ⋊ C7×D45
SylowC9 ⋊ C7×D115
SylowC5 ⋊ C7×D207

Subgroups

subgroupG/H
center, hypercenterC7D1035
commutator, cosocle, hypocenterC5×C9×C23C2×C7
FrattiniC3C7×D345
FittingC5×C7×C9×C23C2
socleC3×C5×C7×C23D3
LCSG ▷ C5×C9×C23
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

3633 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D23×D45, D7×D1035, D161⋊D45, …
maximal normal subgroup ofC7×D23×D45, D7×D1035, D161⋊D45, …
maximal quotient ofC7×Dic1035, C2×C7×D1035

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 15);