Finite Group Databasebeta

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C37×D315 #37552000

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

Aliases

direct productC37×D315
unambiguous semidirect productC5⋊(C37×D63)
unambiguous semidirect productC7⋊(C37×D45)
unambiguous semidirect productC9⋊(C37×D35)

Splittings

Fitting, HallC5×C7×C9×C37 ⋊ C2
derived, HallC5×C7×C9 ⋊ C2×C37
HallC7×C9×C37 ⋊ D5
HallC5×C9×C37 ⋊ D7
HallC5×C7×C37 ⋊ D9
HallC9×C37 ⋊ D35
HallC7×C37 ⋊ D45
HallC5×C37 ⋊ D63
HallC7×C9 ⋊ D5×C37
HallC5×C9 ⋊ D7×C37
HallC5×C7 ⋊ D9×C37
SylowC9 ⋊ C37×D35
SylowC7 ⋊ C37×D45
SylowC5 ⋊ C37×D63

Subgroups

subgroupG/H
center, hypercenterC37D315
commutator, cosocle, hypocenterC5×C7×C9C2×C37
FrattiniC3C37×D105
FittingC5×C7×C9×C37C2
socleC3×C5×C7×C37D3
LCSG ▷ C5×C7×C9
UCSC1 ◁ C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

5883 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 19);