Finite Group Databasebeta

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C3⋊(C25⋊(D29⋊C7)) #44478541

order30450
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C25⋊(D29⋊C7))
unambiguous semidirect productC25⋊(C3⋊(D29⋊C7))
unambiguous semidirect product(C29⋊C7)⋊D75
unambiguous semidirect productD2175⋊C7

Splittings

Fitting, derived, HallC3×C25×C29 ⋊ C2×C7
HallC3×C25×C29⋊C7 ⋊ C2
HallC25×C29⋊C7 ⋊ D3
HallD2175 ⋊ C7
HallC25×C29 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ D25
HallC29⋊C7 ⋊ D75
HallC3×C29 ⋊ C7×D25
HallC3×C25 ⋊ D29⋊C7
SylowC29 ⋊ C7×D75
SylowC25 ⋊ C3⋊(D29⋊C7)
SylowC3 ⋊ C25⋊(D29⋊C7)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C25×C29C2×C7
FrattiniC5C3⋊(C5⋊(D29⋊C7))
socleC3×C5×C29C7×D5
LCSG ▷ C3×C25×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2175

Polycyclic presentation:

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

Conjugacy classes & character table

423 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 25);