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C5×C29×D63 #32912475

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×D63
unambiguous semidirect productC7⋊(C5×D9×C29)
unambiguous semidirect productC9⋊(C5×D7×C29)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C2
derived, HallC7×C9 ⋊ C2×C5×C29
HallC7×C9×C29 ⋊ C2×C5
HallC5×C9×C29 ⋊ D7
HallC5×C7×C29 ⋊ D9
HallC5×C7×C9 ⋊ C2×C29
HallC9×C29 ⋊ C5×D7
HallC7×C29 ⋊ C5×D9
HallC5×C9 ⋊ D7×C29
HallC5×C7 ⋊ D9×C29
SylowC9 ⋊ C5×D7×C29
SylowC7 ⋊ C5×D9×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29D63
commutator, cosocle, hypocenterC7×C9C2×C5×C29
FrattiniC3C5×C29×D21
FittingC5×C7×C9×C29C2
socleC3×C5×C7×C29D3
LCSG ▷ C7×C9
UCSC1 ◁ C5×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D29×D63, C5×D7×D9×C29, C5×D63⋊D29, …
maximal normal subgroup ofC5×D29×D63, C5×D7×D9×C29, C5×D63⋊D29, …
maximal quotient ofC5×C29×Dic63, C2×C5×C29×D63

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 13);