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C5×C7×D261 #32912474

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D261
unambiguous semidirect productC9⋊(C5×C7×D29)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C2
derived, HallC9×C29 ⋊ C2×C5×C7
HallC7×C9×C29 ⋊ C2×C5
HallC5×C9×C29 ⋊ C2×C7
HallC5×C7×C29 ⋊ D9
HallC5×C7×C9 ⋊ D29
HallC7×C29 ⋊ C5×D9
HallC5×C29 ⋊ C7×D9
HallC7×C9 ⋊ C5×D29
HallC5×C9 ⋊ C7×D29
SylowC29 ⋊ C5×C7×D9
SylowC9 ⋊ C5×C7×D29

Subgroups

subgroupG/H
center, hypercenterC5×C7D261
commutator, cosocle, hypocenterC9×C29C2×C5×C7
FrattiniC3C5×C7×D87
FittingC5×C7×C9×C29C2
socleC3×C5×C7×C29D3
LCSG ▷ C9×C29
UCSC1 ◁ C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D9×D29, C5×D7×D261, C5×D63⋊D29, …
maximal normal subgroup ofC5×C7×D9×D29, C5×D7×D261, C5×D63⋊D29, …
maximal quotient ofC5×C7×Dic261, C2×C5×C7×D261

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 12);