Finite Group Databasebeta

← Prev (#37551988) Next (#37551990) →

C5×C9×D259 #37551989

order23310
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D259

Splittings

Fitting, HallC5×C7×C9×C37 ⋊ C2
derived, HallC7×C37 ⋊ C2×C5×C9
HallC7×C9×C37 ⋊ C2×C5
HallC5×C9×C37 ⋊ D7
HallC5×C7×C37 ⋊ C2×C9
HallC9×C37 ⋊ C5×D7
HallC5×C7×C9 ⋊ D37
HallC5×C37 ⋊ C9×D7
HallC7×C9 ⋊ C5×D37
SylowC37 ⋊ C5×C9×D7
HallC5×C7 ⋊ C9×D37
SylowC7 ⋊ C5×C9×D37

Subgroups

subgroupG/H
center, hypercenterC5×C9D259
commutator, hypocenterC7×C37C2×C5×C9
FrattiniC3C3×C5×D259
FittingC5×C7×C9×C37C2
socleC3×C5×C7×C37C2×C3
prime radicalC3×C5×D259C3
cosocleC3×C7×C37C2×C3×C5
LCSG ▷ C7×C37
UCSC1 ◁ C5×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

5895 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 8);