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C9×D5×C29⋊C7 #32912482

order18270
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D5×C29⋊C7
unambiguous semidirect productC5⋊(C2×C9×C29⋊C7)
unambiguous semidirect product(D5×C29)⋊(C7×C9)
unambiguous semidirect product(C9×D5×C29)⋊C7

Splittings

Fitting, HallC5×C9×C29 ⋊ C2×C7
derived, HallC5×C29 ⋊ C2×C7×C9
HallC5×C9×C29⋊C7 ⋊ C2
HallC9×D5×C29 ⋊ C7
HallC5×C29⋊C7 ⋊ C2×C9
HallD5×C29 ⋊ C7×C9
HallC9×C29 ⋊ C7×D5
HallC5×C9 ⋊ C2×C29⋊C7
SylowC29 ⋊ C7×C9×D5
SylowC5 ⋊ C2×C9×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC9D5×C29⋊C7
commutator, hypocenterC5×C29C2×C7×C9
FrattiniC3C3×D5×C29⋊C7
FittingC5×C9×C29C2×C7
socle, cosocleC3×C5×C29C2×C3×C7
prime radicalC3×D5×C29⋊C7C3
LCSG ▷ C5×C29
UCSC1 ◁ C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1305

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×#10596816⋊C7, C9×AGL(1,𝔽5)×C29⋊C7, C9×D5×D29⋊C7, …
maximal normal subgroup ofC9×#10596816⋊C7, C9×AGL(1,𝔽5)×C29⋊C7, C9×D5×D29⋊C7, …
maximal quotient ofC9×Dic5×C29⋊C7, C2×C9×D5×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 20);