Finite Group Databasebeta

← Prev (#38735923) Next (#38735925) →

C17×D15×C49 #38735924

order24990
automorphism?
homologyAbelianization (H1) = C2×C17×C49 · Schur multiplier (H2) = C1

Aliases

direct productC17×D15×C49
unambiguous semidirect productC3⋊(D5×C17×C49)
unambiguous semidirect productC5⋊(D3×C17×C49)

Splittings

Fitting, HallC3×C5×C17×C49 ⋊ C2
derived, HallC3×C5 ⋊ C2×C17×C49
HallC5×C17×C49 ⋊ D3
HallC3×C17×C49 ⋊ D5
HallC3×C5×C49 ⋊ C2×C17
HallC3×C5×C17 ⋊ C2×C49
HallC5×C49 ⋊ D3×C17
HallC3×C49 ⋊ D5×C17
HallC5×C17 ⋊ D3×C49
HallC3×C17 ⋊ D5×C49
SylowC5 ⋊ D3×C17×C49
SylowC3 ⋊ D5×C17×C49

Subgroups

subgroupG/H
center, hypercenterC17×C49D15
commutator, hypocenterC3×C5C2×C17×C49
FrattiniC7C7×C17×D15
FittingC3×C5×C17×C49C2
socleC3×C5×C7×C17C2×C7
prime radicalC7×C17×D15C7
cosocleC3×C5×C7C2×C7×C17
LCSG ▷ C3×C5
UCSC1 ◁ C17×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12495

Conjugacy classes & character table

7497 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 14);