Finite Group Databasebeta

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C3×C5×D1045 #44535527

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1045
unambiguous semidirect productC5⋊(C3×C5×D209)

Splittings

Fitting, socle, HallC3×C52×C11×C19 ⋊ C2
derivedC5×C11×C19 ⋊ C2×C3×C5
HallC52×C11×C19 ⋊ C2×C3
HallC3×C52×C19 ⋊ D11
HallC3×C52×C11 ⋊ D19
HallC3×C11×C19 ⋊ C5×D5
HallC52×C19 ⋊ C3×D11
HallC52×C11 ⋊ C3×D19
HallC11×C19 ⋊ C3×C5×D5
HallC3×C52 ⋊ D209
HallC3×C19 ⋊ C5×D55
HallC3×C11 ⋊ C5×D95
SylowC52 ⋊ C3×D209
SylowC19 ⋊ C3×C5×D55
SylowC11 ⋊ C3×C5×D95

Subgroups

subgroupG/H
center, hypercenterC3×C5D1045
commutator, cosocle, hypocenterC5×C11×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C11×C19C2
LCSG ▷ C5×C11×C19
UCSC1 ◁ C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

7860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 100);