Finite Group Databasebeta

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C5×D2331 #37551997

order23310
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2331
unambiguous semidirect productC7⋊(C5×D333)
unambiguous semidirect productC9⋊(C5×D259)
unambiguous semidirect productC37⋊(C5×D63)

Splittings

Fitting, HallC5×C7×C9×C37 ⋊ C2
derived, HallC7×C9×C37 ⋊ C2×C5
HallC5×C9×C37 ⋊ D7
HallC5×C7×C37 ⋊ D9
HallC9×C37 ⋊ C5×D7
HallC5×C7×C9 ⋊ D37
HallC7×C37 ⋊ C5×D9
HallC5×C37 ⋊ D63
HallC7×C9 ⋊ C5×D37
HallC5×C9 ⋊ D259
SylowC37 ⋊ C5×D63
HallC5×C7 ⋊ D333
SylowC9 ⋊ C5×D259
SylowC7 ⋊ C5×D333

Subgroups

subgroupG/H
center, hypercenterC5D2331
commutator, cosocle, hypocenterC7×C9×C37C2×C5
FrattiniC3C5×D777
FittingC5×C7×C9×C37C2
socleC3×C5×C7×C37D3
LCSG ▷ C7×C9×C37
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

5835 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 16);