Finite Group Databasebeta

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C5×D15×C29⋊C7 #44478564

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

Aliases

direct productC5×D15×C29⋊C7
unambiguous semidirect productC3⋊(C5×D5×C29⋊C7)
unambiguous semidirect productC5⋊(C5×D3×C29⋊C7)
unambiguous semidirect product(C29×D15)⋊(C5×C7)
unambiguous semidirect product(C5×C29×D15)⋊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×C29×D15 ⋊ C7
HallC52×C29 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ C5×D5
HallC3×C29 ⋊ C5×C7×D5
HallC3×C52 ⋊ C2×C29⋊C7
SylowC29 ⋊ C5×C7×D15
SylowC52 ⋊ D3×C29⋊C7
SylowC3 ⋊ C5×D5×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC5D15×C29⋊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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 48);