Finite Group Databasebeta

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C59×D285 #46777523

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

Aliases

direct productC59×D285
unambiguous semidirect productC3⋊(C59×D95)
unambiguous semidirect productC5⋊(C59×D57)
unambiguous semidirect productC19⋊(D15×C59)

Splittings

Fitting, socle, HallC3×C5×C19×C59 ⋊ C2
derived, HallC3×C5×C19 ⋊ C2×C59
HallC5×C19×C59 ⋊ D3
HallC3×C19×C59 ⋊ D5
HallC19×C59 ⋊ D15
HallC3×C5×C59 ⋊ D19
HallC5×C59 ⋊ D57
HallC3×C59 ⋊ D95
HallC5×C19 ⋊ D3×C59
HallC3×C19 ⋊ D5×C59
SylowC19 ⋊ D15×C59
HallC3×C5 ⋊ D19×C59
SylowC5 ⋊ C59×D57
SylowC3 ⋊ C59×D95

Subgroups

subgroupG/H
center, hypercenterC59D285
commutator, cosocle, hypocenterC3×C5×C19C2×C59
FrattiniC1G
Fitting, socleC3×C5×C19×C59C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16815

Conjugacy classes & character table

8496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33630, 16);