Finite Group Databasebeta

C9×D35⋊D23 #44394385

order28980
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC9×D35⋊D23
unambiguous semidirect productD115⋊(C9×D7)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C22
derived, HallC5×C7×C23 ⋊ C22×C9
HallC7×C9×C23 ⋊ C2×D5
HallC5×C9×C23 ⋊ C2×D7
HallC5×C7×C9 ⋊ C2×D23
HallC9×C23 ⋊ D5×D7
HallC7×C23 ⋊ C2×C9×D5
HallC5×C23 ⋊ C2×C9×D7
HallC7×C9 ⋊ D5×D23
HallC5×C9 ⋊ D7×D23
HallC5×C7 ⋊ C2×C9×D23
SylowC23 ⋊ C9×D5×D7
SylowC7 ⋊ C9×D5×D23
SylowC5 ⋊ C9×D7×D23

Subgroups

subgroupG/H
center, hypercenterC9D35⋊D23
commutator, hypocenterC5×C7×C23C22×C9
FrattiniC3C3×D35⋊D23
FittingC5×C7×C9×C23C22
socle, cosocleC3×C5×C7×C23C22×C3
prime radicalC3×D35⋊D23C3
LCSG ▷ C5×C7×C23
UCSC1 ◁ C9

120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

2061 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 54);