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C5×D29×C7⋊C9 #32912488

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D29×C7⋊C9
unambiguous semidirect productC29⋊(C2×C5×C7⋊C9)
unambiguous semidirect product(C7×D29)⋊(C5×C9)
unambiguous semidirect product(C5×C7×D29)⋊C9

Splittings

derived, HallC7×C29 ⋊ C2×C5×C9
HallC5×C29×C7⋊C9 ⋊ C2
HallC5×C7×D29 ⋊ C9
HallC29×C7⋊C9 ⋊ C2×C5
HallC5×C7×C29 ⋊ C2×C9
HallC7×D29 ⋊ C5×C9
HallC5×C29 ⋊ C2×C7⋊C9
HallC5×C7 ⋊ C9×D29
SylowC29 ⋊ C2×C5×C7⋊C9
SylowC7 ⋊ C5×C9×D29

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)×D29
commutator, hypocenterC7×C29C2×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)×D29
Fitting, socleC3×C5×C7×C29C2×C3
prime radicalC3×C5×C7×D29C3
cosocleC3×C7×C29C2×C3×C5
LCSG ▷ C7×C29
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

1200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×(C7⋊C9)⋊#1181, C5×D29×D7⋊C9, C5×C7⋊C9×#1181, …
maximal normal subgroup ofC5×(C7⋊C9)⋊#1181, C5×D29×D7⋊C9, C5×C7⋊C9×#1181, …
maximal quotient ofC5×C7⋊C9×Dic29, C2×C5×D29×C7⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 26);