Finite Group Databasebeta

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C13×D15×C49 #34062024

order19110
automorphism?
homologyAbelianization (H1) = C2×C13×C49 · Schur multiplier (H2) = C1

Aliases

direct productC13×D15×C49
unambiguous semidirect productC3⋊(D5×C13×C49)
unambiguous semidirect productC5⋊(D3×C13×C49)

Splittings

Fitting, HallC3×C5×C13×C49 ⋊ C2
derived, HallC3×C5 ⋊ C2×C13×C49
HallC5×C13×C49 ⋊ D3
HallC3×C13×C49 ⋊ D5
HallC3×C5×C49 ⋊ C2×C13
HallC5×C49 ⋊ D3×C13
HallC3×C5×C13 ⋊ C2×C49
HallC3×C49 ⋊ D5×C13
HallC5×C13 ⋊ D3×C49
HallC3×C13 ⋊ D5×C49
SylowC5 ⋊ D3×C13×C49
SylowC3 ⋊ D5×C13×C49

Subgroups

subgroupG/H
center, hypercenterC13×C49D15
commutator, hypocenterC3×C5C2×C13×C49
FrattiniC7C7×C13×D15
FittingC3×C5×C13×C49C2
socleC3×C5×C7×C13C2×C7
prime radicalC7×C13×D15C7
cosocleC3×C5×C7C2×C7×C13
LCSG ▷ C3×C5
UCSC1 ◁ C13×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

5733 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13×D15×C49, C13×D15×D49, D15×D637, …
maximal normal subgroup ofD13×D15×C49, C13×D15×D49, D15×D637, …
maximal quotient ofC13×C49×Dic15, C2×C13×D15×C49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 17);