Finite Group Databasebeta

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C5×C3⋊(C5⋊(D29⋊C7)) #44478563

order30450
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C5⋊(D29⋊C7))
unambiguous semidirect productC3⋊(C5×C5⋊(D29⋊C7))
unambiguous semidirect productC5⋊(C5×C3⋊(D29⋊C7))
unambiguous semidirect product(C29⋊C7)⋊(C5×D15)
unambiguous semidirect productD435⋊(C5×C7)
unambiguous semidirect product(C5×D435)⋊C7

Splittings

Fitting, socle, HallC3×C52×C29 ⋊ C2×C7
derivedC3×C5×C29 ⋊ C2×C5×C7
HallC3×C52×C29⋊C7 ⋊ C2
HallC52×C29⋊C7 ⋊ D3
HallC5×D435 ⋊ C7
HallC52×C29 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ C5×D5
HallC29⋊C7 ⋊ C5×D15
HallC3×C29 ⋊ C5×C7×D5
HallC3×C52 ⋊ D29⋊C7
SylowC29 ⋊ C5×C7×D15
SylowC52 ⋊ C3⋊(D29⋊C7)
SylowC3 ⋊ C5×C5⋊(D29⋊C7)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C5⋊(D29⋊C7))
commutator, cosocle, hypocenterC3×C5×C29C2×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C29C2×C7
LCSG ▷ C3×C5×C29
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 870

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 47);