Finite Group Databasebeta

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C5×C49×D13⋊C3 #34062028

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×C49×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×C49)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C49)
unambiguous semidirect product(C5×D13)⋊(C3×C49)

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C49
HallC5×C13⋊C3×C49 ⋊ C2
HallC5×D13×C49 ⋊ C3
HallC13⋊C3×C49 ⋊ C2×C5
HallD13×C49 ⋊ C3×C5
HallC13×C49 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C49
HallC5×D13 ⋊ C3×C49
HallC5×C13 ⋊ C2×C3×C49
HallC13⋊C3 ⋊ C2×C5×C49
HallD13 ⋊ C3×C5×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49D13⋊C3
commutator, hypocenterC13C2×C3×C5×C49
FrattiniC7C5×C7×D13⋊C3
FittingC5×C13×C49C2×C3
socleC5×C7×C13C2×C3×C7
prime radicalC5×C7×D13⋊C3C7
cosocleC7×C13C2×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C5×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C49×AGL(1,𝔽13), C5×#21439458, C5×D13⋊C3×D49, …
maximal normal subgroup ofC5×C49×AGL(1,𝔽13), C5×#21439458, C5×D13⋊C3×D49, …
maximal quotient ofC5×C49×Dic13⋊C3, C2×C5×C49×D13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 21);