Finite Group Databasebeta

← Prev (#38788908) Next (#38788910) →

C5×C7×D369 #38788909

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

Aliases

direct productC5×C7×D369
unambiguous semidirect productC9⋊(C5×C7×D41)

Splittings

Fitting, HallC5×C7×C9×C41 ⋊ C2
derived, HallC9×C41 ⋊ C2×C5×C7
HallC7×C9×C41 ⋊ C2×C5
HallC5×C9×C41 ⋊ C2×C7
HallC5×C7×C41 ⋊ D9
HallC5×C7×C9 ⋊ D41
HallC7×C41 ⋊ C5×D9
HallC5×C41 ⋊ C7×D9
HallC7×C9 ⋊ C5×D41
HallC5×C9 ⋊ C7×D41
SylowC41 ⋊ C5×C7×D9
SylowC9 ⋊ C5×C7×D41

Subgroups

subgroupG/H
center, hypercenterC5×C7D369
commutator, cosocle, hypocenterC9×C41C2×C5×C7
FrattiniC3C5×C7×D123
FittingC5×C7×C9×C41C2
socleC3×C5×C7×C41D3
LCSG ▷ C9×C41
UCSC1 ◁ C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

6510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 13);