Finite Group Databasebeta

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C3×C47×D85 #37561789

order23970
automorphism?
homologyAbelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47×D85
unambiguous semidirect productC5⋊(C3×D17×C47)
unambiguous semidirect productC17⋊(C3×D5×C47)

Splittings

Fitting, socle, HallC3×C5×C17×C47 ⋊ C2
derived, HallC5×C17 ⋊ C2×C3×C47
HallC5×C17×C47 ⋊ C2×C3
HallC3×C17×C47 ⋊ D5
HallC17×C47 ⋊ C3×D5
HallC3×C5×C47 ⋊ D17
HallC3×C5×C17 ⋊ C2×C47
HallC5×C47 ⋊ C3×D17
HallC3×C17 ⋊ D5×C47
SylowC17 ⋊ C3×D5×C47
HallC3×C5 ⋊ D17×C47
SylowC5 ⋊ C3×D17×C47

Subgroups

subgroupG/H
center, hypercenterC3×C47D85
commutator, cosocle, hypocenterC5×C17C2×C3×C47
FrattiniC1G
Fitting, socleC3×C5×C17×C47C2
LCSG ▷ C5×C17
UCSC1 ◁ C3×C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11985

Conjugacy classes & character table

6204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23970, 7);