Finite Group Databasebeta

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C17×D735 #38735926

order24990
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D735
unambiguous semidirect productC3⋊(C17×D245)
unambiguous semidirect productC5⋊(C17×D147)
unambiguous semidirect productC49⋊(C17×D15)

Splittings

Fitting, HallC3×C5×C17×C49 ⋊ C2
derived, HallC3×C5×C49 ⋊ C2×C17
HallC5×C17×C49 ⋊ D3
HallC3×C17×C49 ⋊ D5
HallC17×C49 ⋊ D15
HallC3×C5×C17 ⋊ D49
HallC5×C49 ⋊ D3×C17
HallC3×C49 ⋊ D5×C17
HallC5×C17 ⋊ D147
HallC3×C17 ⋊ D245
SylowC49 ⋊ C17×D15
HallC3×C5 ⋊ C17×D49
SylowC5 ⋊ C17×D147
SylowC3 ⋊ C17×D245

Subgroups

subgroupG/H
center, hypercenterC17D735
commutator, cosocle, hypocenterC3×C5×C49C2×C17
FrattiniC7C17×D105
FittingC3×C5×C17×C49C2
socleC3×C5×C7×C17D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12495

Conjugacy classes & character table

6273 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 16);