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C3⋊(C3⋊(C5⋊(D29⋊C7))) #32912505

order18270
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(C5⋊(D29⋊C7)))
unambiguous semidirect productC5⋊(C3⋊(C3⋊(D29⋊C7)))
unambiguous semidirect product(C29⋊C7)⋊(C3⋊D15)
unambiguous semidirect product(C3⋊D435)⋊C7

Splittings

Fitting, socle, derived, HallC32×C5×C29 ⋊ C2×C7
HallC32×C5×C29⋊C7 ⋊ C2
HallC3⋊D435 ⋊ C7
HallC32×C29⋊C7 ⋊ D5
HallC5×C29⋊C7 ⋊ C3⋊D3
HallC32×C29 ⋊ C7×D5
HallC29⋊C7 ⋊ C3⋊D15
HallC5×C29 ⋊ C7×C3⋊D3
HallC32×C5 ⋊ D29⋊C7
SylowC29 ⋊ C7×C3⋊D15
SylowC32 ⋊ C5⋊(D29⋊C7)
SylowC5 ⋊ C3⋊(C3⋊(D29⋊C7))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C29C2×C7
LCSG ▷ C32×C5×C29
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1305

Polycyclic presentation:

2,7,3^2,5,29|c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^28,f^b=f^16

Conjugacy classes & character table

258 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#19104885⋊C7, #19104886⋊C7, D3×C3⋊(C5⋊(D29⋊C7)), …
maximal normal subgroup of#19104885⋊C7, #19104886⋊C7, D3×C3⋊(C5⋊(D29⋊C7)), …
maximal quotient ofC3⋊(C3⋊(Dic145⋊C7)), C2×C3⋊(C3⋊(C5⋊(D29⋊C7)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 43);