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C5×C9×#10621729 #44477722

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

Aliases

direct productC5×C9×#10621729

Splittings

Fitting, HallC5×C9×C132 ⋊ C4
derived, SylowC132 ⋊ C4×C5×C9
HallC9×C132 ⋊ C4×C5
HallC5×C132 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9#10621729
commutator, hypocenterC132C4×C5×C9
FrattiniC3C3×C5×#10621729
FittingC5×C9×C132C4
socleC3×C5×C132C3×C4
prime radicalC3×C5×C13⋊D13C2×C3
cosocleC3×C13⋊D13C2×C3×C5
LCSG ▷ C132
UCSC1 ◁ C5×C9

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1170

Conjugacy classes & character table

2070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 311);