Finite Group Databasebeta

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C59×C5⋊(D19⋊C3) #46777530

order33630
automorphism?
homologyAbelianization (H1) = C2×C3×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×C5⋊(D19⋊C3)
unambiguous semidirect productC5⋊(C59×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D5×C59)
unambiguous semidirect productD95⋊(C3×C59)
unambiguous semidirect product(C59×D95)⋊C3

Splittings

Fitting, socle, HallC5×C19×C59 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C3×C59
HallC5×C19⋊C3×C59 ⋊ C2
HallC59×D95 ⋊ C3
HallC19⋊C3×C59 ⋊ D5
HallC19×C59 ⋊ C3×D5
HallC5×C59 ⋊ D19⋊C3
HallC5×C19⋊C3 ⋊ C2×C59
HallD95 ⋊ C3×C59
HallC19⋊C3 ⋊ D5×C59
SylowC19 ⋊ C3×D5×C59
SylowC5 ⋊ C59×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC59C5⋊(D19⋊C3)
commutator, cosocle, hypocenterC5×C19C2×C3×C59
FrattiniC1G
Fitting, socleC5×C19×C59C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5605

Conjugacy classes & character table

1593 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33630, 23);