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D19⋊C3×D65 #28414835

order14820
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD19⋊C3×D65
unambiguous semidirect productD19⋊(C3×D65)
unambiguous semidirect product(C5×D19⋊C3)⋊D13
unambiguous semidirect product(C13×D19⋊C3)⋊D5

Splittings

Fitting, socle, derived, HallC5×C13×C19 ⋊ C22×C3
HallD19×D65 ⋊ C3
HallC5×C13×C19⋊C3 ⋊ C22
HallC13×C19⋊C3 ⋊ C2×D5
HallC5×C19⋊C3 ⋊ C2×D13
HallC13×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×C3×D13
HallC5×C13 ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×D65
SylowC19 ⋊ C2×C3×D65
SylowC13 ⋊ D5×D19⋊C3
SylowC5 ⋊ D13×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C19C22×C3
LCSG ▷ C5×C13×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1235

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 121);