Finite Group Databasebeta

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C7×C9×D205 #38788905

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

Aliases

direct productC7×C9×D205
unambiguous semidirect productC5⋊(C7×C9×D41)
unambiguous semidirect productC41⋊(C7×C9×D5)

Splittings

Fitting, HallC5×C7×C9×C41 ⋊ C2
derived, HallC5×C41 ⋊ C2×C7×C9
HallC7×C9×C41 ⋊ D5
HallC5×C9×C41 ⋊ C2×C7
HallC5×C7×C41 ⋊ C2×C9
HallC9×C41 ⋊ C7×D5
HallC5×C7×C9 ⋊ D41
HallC7×C41 ⋊ C9×D5
HallC5×C9 ⋊ C7×D41
SylowC41 ⋊ C7×C9×D5
HallC5×C7 ⋊ C9×D41
SylowC5 ⋊ C7×C9×D41

Subgroups

subgroupG/H
center, hypercenterC7×C9D205
commutator, hypocenterC5×C41C2×C7×C9
FrattiniC3C3×C7×D205
FittingC5×C7×C9×C41C2
socleC3×C5×C7×C41C2×C3
prime radicalC3×C7×D205C3
cosocleC3×C5×C41C2×C3×C7
LCSG ▷ C5×C41
UCSC1 ◁ C7×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

6552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 9);