Finite Group Databasebeta

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C3×C5×D1235 #49150322

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1235
unambiguous semidirect productC5⋊(C3×C5×D247)

Splittings

Fitting, socle, HallC3×C52×C13×C19 ⋊ C2
derivedC5×C13×C19 ⋊ C2×C3×C5
HallC52×C13×C19 ⋊ C2×C3
HallC3×C52×C19 ⋊ D13
HallC3×C52×C13 ⋊ D19
HallC3×C13×C19 ⋊ C5×D5
HallC52×C19 ⋊ C3×D13
HallC52×C13 ⋊ C3×D19
HallC13×C19 ⋊ C3×C5×D5
HallC3×C52 ⋊ D247
HallC3×C19 ⋊ C5×D65
HallC3×C13 ⋊ C5×D95
SylowC52 ⋊ C3×D247
SylowC19 ⋊ C3×C5×D65
SylowC13 ⋊ C3×C5×D95

Subgroups

subgroupG/H
center, hypercenterC3×C5D1235
commutator, cosocle, hypocenterC5×C13×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C13×C19C2
LCSG ▷ C5×C13×C19
UCSC1 ◁ C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7410

Conjugacy classes & character table

9285 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 148);