Finite Group Databasebeta

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C3×C59×D85 #44473854

order30090
automorphism?
homologyAbelianization (H1) = C2×C3×C59 · Schur multiplier (H2) = C1

Aliases

direct productC3×C59×D85
unambiguous semidirect productC5⋊(C3×D17×C59)
unambiguous semidirect productC17⋊(C3×D5×C59)

Splittings

Fitting, socle, HallC3×C5×C17×C59 ⋊ C2
derived, HallC5×C17 ⋊ C2×C3×C59
HallC5×C17×C59 ⋊ C2×C3
HallC3×C17×C59 ⋊ D5
HallC17×C59 ⋊ C3×D5
HallC3×C5×C59 ⋊ D17
HallC5×C59 ⋊ C3×D17
HallC3×C5×C17 ⋊ C2×C59
HallC3×C17 ⋊ D5×C59
SylowC17 ⋊ C3×D5×C59
HallC3×C5 ⋊ D17×C59
SylowC5 ⋊ C3×D17×C59

Subgroups

subgroupG/H
center, hypercenterC3×C59D85
commutator, cosocle, hypocenterC5×C17C2×C3×C59
FrattiniC1G
Fitting, socleC3×C5×C17×C59C2
LCSG ▷ C5×C17
UCSC1 ◁ C3×C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15045

Conjugacy classes & character table

7788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30090, 7);