Finite Group Databasebeta

← Prev (#44477719) Next (#44477721) →

C5×C9×C13×#261 #44477720

order30420
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×C13×#261

Splittings

Fitting, HallC5×C9×C132 ⋊ C4
derivedC13 ⋊ C4×C5×C9×C13
HallC9×C132 ⋊ C4×C5
HallC5×C132 ⋊ C4×C9
SylowC132 ⋊ C4×C5×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9×C13#261
commutator, hypocenterC13C4×C5×C9×C13
FrattiniC3C3×C5×C13×#261
FittingC5×C9×C132C4
socleC3×C5×C132C3×C4
prime radicalC3×C5×C13×D13C2×C3
cosocleC3×D13C2×C3×C5×C13
LCSG ▷ C13
UCSC1 ◁ C5×C9×C13

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

4095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 309);