Finite Group Databasebeta

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C5×D3135 #44535539

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

Aliases

direct productC5×D3135
unambiguous semidirect productC3⋊(C5×D1045)
unambiguous semidirect productC5⋊(C5×D627)
unambiguous semidirect productC19⋊(C5×D165)

Splittings

Fitting, socle, HallC3×C52×C11×C19 ⋊ C2
derivedC3×C5×C11×C19 ⋊ C2×C5
HallC52×C11×C19 ⋊ D3
HallC3×C52×C19 ⋊ D11
HallC3×C52×C11 ⋊ D19
HallC3×C11×C19 ⋊ C5×D5
HallC52×C19 ⋊ D33
HallC52×C11 ⋊ D57
HallC11×C19 ⋊ C5×D15
HallC3×C52 ⋊ D209
HallC3×C19 ⋊ C5×D55
HallC3×C11 ⋊ C5×D95
SylowC52 ⋊ D627
SylowC19 ⋊ C5×D165
SylowC11 ⋊ C5×D285
SylowC3 ⋊ C5×D1045

Subgroups

subgroupG/H
center, hypercenterC5D3135
commutator, cosocle, hypocenterC3×C5×C11×C19C2×C5
FrattiniC1G
Fitting, socleC3×C52×C11×C19C2
LCSG ▷ C3×C5×C11×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

7845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 112);