Finite Group Databasebeta

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C19⋊C3×D295 #46777529

order33630
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC19⋊C3×D295
unambiguous semidirect productC5⋊(C19⋊C3×D59)
unambiguous semidirect productC59⋊(D5×C19⋊C3)
unambiguous semidirect product(C19×D295)⋊C3

Splittings

Fitting, socle, derived, HallC5×C19×C59 ⋊ C2×C3
HallC5×C19⋊C3×C59 ⋊ C2
HallC19×D295 ⋊ C3
HallC19⋊C3×C59 ⋊ D5
HallC19×C59 ⋊ C3×D5
HallC5×C59 ⋊ C2×C19⋊C3
HallC5×C19⋊C3 ⋊ D59
HallC5×C19 ⋊ C3×D59
SylowC59 ⋊ D5×C19⋊C3
SylowC19 ⋊ C3×D295
SylowC5 ⋊ C19⋊C3×D59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C59C2×C3
LCSG ▷ C5×C19×C59
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5605

Conjugacy classes & character table

1341 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33630, 22);