Finite Group Databasebeta

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C5×C7×C9×#261 #30655104

order16380
isoclinismisoclinic class of #261
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C9×#261

Splittings

Fitting, HallC5×C7×C9×C13 ⋊ C4
derived, SylowC13 ⋊ C4×C5×C7×C9
HallC7×C9×C13 ⋊ C4×C5
HallC5×C9×C13 ⋊ C4×C7
HallC5×C7×C13 ⋊ C4×C9
HallC9×C13 ⋊ C4×C5×C7
HallC7×C13 ⋊ C4×C5×C9
HallC5×C13 ⋊ C4×C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C7×C9#261
commutator, hypocenterC13C4×C5×C7×C9
FrattiniC3C3×C5×C7×#261
FittingC5×C7×C9×C13C4
socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13C2×C3
cosocleC3×D13C2×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C5×C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4095

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 154);