Finite Group Databasebeta

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C52×C13×D19⋊C3 #49150263

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C13 · Schur multiplier (H2) = C5

Aliases

direct productC52×C13×D19⋊C3
unambiguous semidirect productD19⋊(C3×C52×C13)
unambiguous semidirect product(C19⋊C3)⋊(C2×C52×C13)
unambiguous semidirect product(C5×D19)⋊(C3×C5×C13)

Splittings

Fitting, socle, HallC52×C13×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C52×C13
HallC52×C13×C19⋊C3 ⋊ C2
HallC52×C13×D19 ⋊ C3
HallC52×C19⋊C3 ⋊ C2×C13
HallC52×D19 ⋊ C3×C13
HallC13×C19⋊C3 ⋊ C2×C52
HallC13×D19 ⋊ C3×C52
HallC52×C19 ⋊ C2×C3×C13
HallC13×C19 ⋊ C2×C3×C52
HallC19⋊C3 ⋊ C2×C52×C13
HallD19 ⋊ C3×C52×C13

Subgroups

subgroupG/H
center, hypercenterC52×C13D19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C52×C13
FrattiniC1G
Fitting, socleC52×C13×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C52×C13

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 89);