Finite Group Databasebeta

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C17×D705 #37561796

order23970
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D705
unambiguous semidirect productC3⋊(C17×D235)
unambiguous semidirect productC5⋊(C17×D141)
unambiguous semidirect productC47⋊(C17×D15)

Splittings

Fitting, socle, HallC3×C5×C17×C47 ⋊ C2
derived, HallC3×C5×C47 ⋊ C2×C17
HallC5×C17×C47 ⋊ D3
HallC3×C17×C47 ⋊ D5
HallC17×C47 ⋊ D15
HallC3×C5×C17 ⋊ D47
HallC5×C47 ⋊ D3×C17
HallC3×C47 ⋊ D5×C17
HallC5×C17 ⋊ D141
HallC3×C17 ⋊ D235
SylowC47 ⋊ C17×D15
HallC3×C5 ⋊ C17×D47
SylowC5 ⋊ C17×D141
SylowC3 ⋊ C17×D235

Subgroups

subgroupG/H
center, hypercenterC17D705
commutator, cosocle, hypocenterC3×C5×C47C2×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C47C2
LCSG ▷ C3×C5×C47
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11985

Conjugacy classes & character table

6018 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23970, 14);