Finite Group Databasebeta

← Prev (#34062024) Next (#34062026) →

C49×D195 #34062025

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

Aliases

direct productC49×D195
unambiguous semidirect productC3⋊(C49×D65)
unambiguous semidirect productC5⋊(C49×D39)
unambiguous semidirect productC13⋊(D15×C49)

Splittings

Fitting, HallC3×C5×C13×C49 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C49
HallC5×C13×C49 ⋊ D3
HallC3×C13×C49 ⋊ D5
HallC3×C5×C49 ⋊ D13
HallC13×C49 ⋊ D15
HallC5×C49 ⋊ D39
HallC3×C49 ⋊ D65
HallC5×C13 ⋊ D3×C49
HallC3×C13 ⋊ D5×C49
HallC3×C5 ⋊ D13×C49
SylowC13 ⋊ D15×C49
SylowC5 ⋊ C49×D39
SylowC3 ⋊ C49×D65

Subgroups

subgroupG/H
center, hypercenterC49D195
commutator, hypocenterC3×C5×C13C2×C49
FrattiniC7C7×D195
FittingC3×C5×C13×C49C2
socle, cosocleC3×C5×C7×C13C2×C7
prime radicalC7×D195C7
LCSG ▷ C3×C5×C13
UCSC1 ◁ C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13×D15×C49, D49×D195, D637⋊D15, …
maximal normal subgroup ofD13×D15×C49, D49×D195, D637⋊D15, …
maximal quotient ofC49×Dic195, C2×C49×D195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 18);