Finite Group Databasebeta

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C19×C25×D13⋊C3 #49150200

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C19×C25 · Schur multiplier (H2) = C1

Aliases

direct productC19×C25×D13⋊C3
unambiguous semidirect productD13⋊(C3×C19×C25)
unambiguous semidirect product(C13⋊C3)⋊(C2×C19×C25)
unambiguous semidirect product(C25×D13)⋊(C3×C19)

Splittings

Fitting, HallC13×C19×C25 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C19×C25
HallC19×C25×C13⋊C3 ⋊ C2
HallC19×C25×D13 ⋊ C3
HallC25×C13⋊C3 ⋊ C2×C19
HallC19×C13⋊C3 ⋊ C2×C25
HallC25×D13 ⋊ C3×C19
HallC19×D13 ⋊ C3×C25
HallC13×C25 ⋊ C2×C3×C19
HallC13×C19 ⋊ C2×C3×C25
HallC13⋊C3 ⋊ C2×C19×C25
HallD13 ⋊ C3×C19×C25

Subgroups

subgroupG/H
center, hypercenterC19×C25D13⋊C3
commutator, hypocenterC13C2×C3×C19×C25
FrattiniC5C5×C19×D13⋊C3
FittingC13×C19×C25C2×C3
socleC5×C13×C19C2×C3×C5
prime radicalC5×C19×D13⋊C3C5
cosocleC5×C13C2×C3×C5×C19
LCSG ▷ C13
UCSC1 ◁ C19×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 26);