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C49×C5⋊(D13⋊C3) #34062044

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

Aliases

direct productC49×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(C49×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D5×C49)
unambiguous semidirect productD65⋊(C3×C49)

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C49
HallC5×C13⋊C3×C49 ⋊ C2
HallC49×D65 ⋊ C3
HallC13⋊C3×C49 ⋊ D5
HallC13×C49 ⋊ C3×D5
HallC5×C49 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ C2×C49
HallD65 ⋊ C3×C49
HallC13⋊C3 ⋊ D5×C49
SylowC13 ⋊ C3×D5×C49
SylowC5 ⋊ C49×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC49C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C2×C3×C49
FrattiniC7C7×C5⋊(D13⋊C3)
FittingC5×C13×C49C2×C3
socle, cosocleC5×C7×C13C2×C3×C7
prime radicalC7×C5⋊(D13⋊C3)C7
LCSG ▷ C5×C13
UCSC1 ◁ C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC49×#63122⋊C3, C49×#63121⋊C3, #50303404, …
maximal normal subgroup ofC49×#63122⋊C3, C49×#63121⋊C3, #50303404, …
maximal quotient ofC49×Dic65⋊C3, C2×C49×C5⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 37);