Finite Group Databasebeta

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C3×C49×D85 #38735917

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×D85
unambiguous semidirect productC5⋊(C3×D17×C49)
unambiguous semidirect productC17⋊(C3×D5×C49)

Splittings

Fitting, HallC3×C5×C17×C49 ⋊ C2
derived, HallC5×C17 ⋊ C2×C3×C49
HallC5×C17×C49 ⋊ C2×C3
HallC3×C17×C49 ⋊ D5
HallC17×C49 ⋊ C3×D5
HallC3×C5×C49 ⋊ D17
HallC3×C5×C17 ⋊ C2×C49
HallC5×C49 ⋊ C3×D17
HallC3×C17 ⋊ D5×C49
SylowC17 ⋊ C3×D5×C49
HallC3×C5 ⋊ D17×C49
SylowC5 ⋊ C3×D17×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49D85
commutator, hypocenterC5×C17C2×C3×C49
FrattiniC7C3×C7×D85
FittingC3×C5×C17×C49C2
socleC3×C5×C7×C17C2×C7
prime radicalC3×C7×D85C7
cosocleC5×C7×C17C2×C3×C7
LCSG ▷ C5×C17
UCSC1 ◁ C3×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12495

Conjugacy classes & character table

6468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 7);