Finite Group Databasebeta

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C5×C13×D285 #49150332

order37050
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D285
unambiguous semidirect productC3⋊(C5×C13×D95)
unambiguous semidirect productC5⋊(C5×C13×D57)
unambiguous semidirect productC19⋊(C5×C13×D15)

Splittings

Fitting, socle, HallC3×C52×C13×C19 ⋊ C2
derivedC3×C5×C19 ⋊ C2×C5×C13
HallC52×C13×C19 ⋊ D3
HallC3×C52×C19 ⋊ C2×C13
HallC3×C52×C13 ⋊ D19
HallC3×C13×C19 ⋊ C5×D5
HallC52×C19 ⋊ D3×C13
HallC52×C13 ⋊ D57
HallC13×C19 ⋊ C5×D15
HallC3×C52 ⋊ C13×D19
HallC3×C19 ⋊ C5×D5×C13
HallC3×C13 ⋊ C5×D95
SylowC52 ⋊ C13×D57
SylowC19 ⋊ C5×C13×D15
SylowC3 ⋊ C5×C13×D95

Subgroups

subgroupG/H
center, hypercenterC5×C13D285
commutator, cosocle, hypocenterC3×C5×C19C2×C5×C13
FrattiniC1G
Fitting, socleC3×C52×C13×C19C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7410

Conjugacy classes & character table

9360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 158);