Finite Group Databasebeta

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C7×D1665 #37551999

order23310
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1665
unambiguous semidirect productC5⋊(C7×D333)
unambiguous semidirect productC9⋊(C7×D185)
unambiguous semidirect productC37⋊(C7×D45)

Splittings

Fitting, HallC5×C7×C9×C37 ⋊ C2
derived, HallC5×C9×C37 ⋊ C2×C7
HallC7×C9×C37 ⋊ D5
HallC5×C7×C37 ⋊ D9
HallC9×C37 ⋊ C7×D5
HallC5×C7×C9 ⋊ D37
HallC7×C37 ⋊ D45
HallC5×C37 ⋊ C7×D9
HallC7×C9 ⋊ D185
HallC5×C9 ⋊ C7×D37
SylowC37 ⋊ C7×D45
HallC5×C7 ⋊ D333
SylowC9 ⋊ C7×D185
SylowC5 ⋊ C7×D333

Subgroups

subgroupG/H
center, hypercenterC7D1665
commutator, cosocle, hypocenterC5×C9×C37C2×C7
FrattiniC3C7×D555
FittingC5×C7×C9×C37C2
socleC3×C5×C7×C37D3
LCSG ▷ C5×C9×C37
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

5838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 18);