Finite Group Databasebeta

← Prev (#38788915) Next (#38788917) →

C7×C9×D41⋊C5 #38788916

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×D41⋊C5
unambiguous semidirect productD41⋊(C5×C7×C9)
unambiguous semidirect product(C41⋊C5)⋊(C2×C7×C9)
unambiguous semidirect product(C9×D41)⋊(C5×C7)
unambiguous semidirect product(C7×C9×D41)⋊C5

Splittings

Fitting, HallC7×C9×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C2×C5×C7×C9
HallC7×C9×C41⋊C5 ⋊ C2
HallC7×C9×D41 ⋊ C5
HallC9×C41⋊C5 ⋊ C2×C7
HallC7×C41⋊C5 ⋊ C2×C9
HallC9×D41 ⋊ C5×C7
HallC7×D41 ⋊ C5×C9
HallC9×C41 ⋊ C2×C5×C7
HallC7×C41 ⋊ C2×C5×C9
HallC41⋊C5 ⋊ C2×C7×C9
HallD41 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC7×C9D41⋊C5
commutator, hypocenterC41C2×C5×C7×C9
FrattiniC3C3×C7×D41⋊C5
FittingC7×C9×C41C2×C5
socleC3×C7×C41C2×C3×C5
prime radicalC3×C7×D41⋊C5C3
cosocleC3×C41C2×C3×C5×C7
LCSG ▷ C41
UCSC1 ◁ C7×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2583

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 20);