Finite Group Databasebeta

← Prev (#49154147) Next (#49154149) →

C5×C17×C49⋊C9 #49154148

order37485
automorphism?
homologyAbelianization (H1) = C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×C49⋊C9
unambiguous semidirect productC49⋊(C5×C9×C17)
unambiguous semidirect product(C5×C49)⋊(C9×C17)
unambiguous semidirect product(C17×C49)⋊(C5×C9)
unambiguous semidirect product(C5×C17×C49)⋊C9

Splittings

derived, SylowC49 ⋊ C5×C9×C17
HallC5×C17×C49 ⋊ C9
HallC17×C49 ⋊ C5×C9
HallC5×C49 ⋊ C9×C17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17C49⋊C3
commutator, hypocenterC49C5×C9×C17
FrattiniC3×C7C5×C17×ΓL(1,𝔽8)
FittingC3×C5×C17×C49C3
socle, prime radicalC3×C5×C7×C17ΓL(1,𝔽8)
cosocleC3×C49C3×C5×C17
LCSG ▷ C49
UCSC1 ◁ C3×C5×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37485

Conjugacy classes & character table

4845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37485, 2);