Finite Group Databasebeta

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C52×C19×D13⋊C3 #49150264

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C19 · Schur multiplier (H2) = C5

Aliases

direct productC52×C19×D13⋊C3
unambiguous semidirect productD13⋊(C3×C52×C19)
unambiguous semidirect product(C13⋊C3)⋊(C2×C52×C19)
unambiguous semidirect product(C5×D13)⋊(C3×C5×C19)

Splittings

Fitting, socle, HallC52×C13×C19 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C52×C19
HallC52×C19×C13⋊C3 ⋊ C2
HallC52×C19×D13 ⋊ C3
HallC52×C13⋊C3 ⋊ C2×C19
HallC19×C13⋊C3 ⋊ C2×C52
HallC52×D13 ⋊ C3×C19
HallC19×D13 ⋊ C3×C52
HallC52×C13 ⋊ C2×C3×C19
HallC13×C19 ⋊ C2×C3×C52
HallC13⋊C3 ⋊ C2×C52×C19
HallD13 ⋊ C3×C52×C19

Subgroups

subgroupG/H
center, hypercenterC52×C19D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C52×C19
FrattiniC1G
Fitting, socleC52×C13×C19C2×C3
LCSG ▷ C13
UCSC1 ◁ C52×C19

128 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, 90);