Finite Group Databasebeta

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C9×C37×D35 #37551992

order23310
automorphism?
homologyAbelianization (H1) = C2×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC9×C37×D35
unambiguous semidirect productC5⋊(C9×D7×C37)

Splittings

Fitting, HallC5×C7×C9×C37 ⋊ C2
derived, HallC5×C7 ⋊ C2×C9×C37
HallC7×C9×C37 ⋊ D5
HallC5×C9×C37 ⋊ D7
HallC5×C7×C37 ⋊ C2×C9
HallC5×C7×C9 ⋊ C2×C37
HallC7×C37 ⋊ C9×D5
HallC5×C37 ⋊ C9×D7
HallC7×C9 ⋊ D5×C37
HallC5×C9 ⋊ D7×C37
SylowC7 ⋊ C9×D5×C37
SylowC5 ⋊ C9×D7×C37

Subgroups

subgroupG/H
center, hypercenterC9×C37D35
commutator, hypocenterC5×C7C2×C9×C37
FrattiniC3C3×C37×D35
FittingC5×C7×C9×C37C2
socleC3×C5×C7×C37C2×C3
prime radicalC3×C37×D35C3
cosocleC3×C5×C7C2×C3×C37
LCSG ▷ C5×C7
UCSC1 ◁ C9×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

6327 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 11);