Finite Group Databasebeta

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C3×C5×D1015 #44478606

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1015
unambiguous semidirect productC5⋊(C3×C5×D203)
unambiguous semidirect productC29⋊(C3×C5×D35)

Splittings

Fitting, socle, HallC3×C52×C7×C29 ⋊ C2
derivedC5×C7×C29 ⋊ C2×C3×C5
HallC52×C7×C29 ⋊ C2×C3
HallC3×C52×C29 ⋊ D7
HallC52×C29 ⋊ C3×D7
HallC3×C7×C29 ⋊ C5×D5
HallC3×C52×C7 ⋊ D29
HallC7×C29 ⋊ C3×C5×D5
HallC52×C7 ⋊ C3×D29
HallC3×C29 ⋊ C5×D35
HallC3×C52 ⋊ D203
SylowC29 ⋊ C3×C5×D35
SylowC52 ⋊ C3×D203
HallC3×C7 ⋊ C5×D145
SylowC7 ⋊ C3×C5×D145

Subgroups

subgroupG/H
center, hypercenterC3×C5D1015
commutator, cosocle, hypocenterC5×C7×C29C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C29C2
LCSG ▷ C5×C7×C29
UCSC1 ◁ C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6090

Conjugacy classes & character table

7635 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 90);