Finite Group Databasebeta

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C2×C5×C13⋊C3×C49 #34062009

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

Aliases

direct productC2×C5×C13⋊C3×C49
unambiguous semidirect product(C2×C13)⋊(C3×C5×C49)
unambiguous semidirect product(C2×C5×C13)⋊(C3×C49)

Splittings

Fitting, HallC2×C5×C13×C49 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C5×C49
HallC5×C13×C49 ⋊ C2×C3
HallC2×C13×C49 ⋊ C3×C5
HallC13×C49 ⋊ C2×C3×C5
HallC2×C5×C13 ⋊ C3×C49
HallC5×C13 ⋊ C2×C3×C49
HallC2×C13 ⋊ C3×C5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C49C13⋊C3
commutator, hypocenterC13C2×C3×C5×C49
FrattiniC7C2×C5×C7×C13⋊C3
FittingC2×C5×C13×C49C3
socleC2×C5×C7×C13C3×C7
prime radicalC2×C5×C7×C13⋊C3C7
cosocleC7×C13C2×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C2×C5×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

3430 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C13⋊C3×C49, C5×C49×Dic13⋊C3, C5×C13⋊C3×Dic49, …
maximal normal subgroup ofC4×C5×C13⋊C3×C49, C5×C49×Dic13⋊C3, C5×C13⋊C3×Dic49, …
maximal quotient ofC4×C5×C13⋊C3×C49, C22×C5×C13⋊C3×C49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 2);