Finite Group Databasebeta

← Prev (#36339238) Next (#36339240) →

C5×C7×C9⋊#595 #36339239

order21420
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C9⋊#595
unambiguous semidirect productC9⋊(C5×C7×#595)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C4
derived, HallC9×C17 ⋊ C4×C5×C7
HallC7×C9×C17 ⋊ C4×C5
HallC5×C9×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ Dic9
HallC5×C7×C9 ⋊ #595
HallC7×C17 ⋊ C5×Dic9
HallC5×C17 ⋊ C7×Dic9
HallC7×C9 ⋊ C5×#595
HallC5×C9 ⋊ C7×#595
SylowC17 ⋊ C5×C7×Dic9
SylowC9 ⋊ C5×C7×#595

Subgroups

subgroupG/H
center, hypercenterC5×C7C9⋊#595
commutator, hypocenterC9×C17C4×C5×C7
FrattiniC3C5×C7×C3⋊#595
FittingC5×C7×C9×C17C4
socleC3×C5×C7×C17Dic3
prime radicalC3×C5×C7×D17D3
cosocleC9×D17C2×C5×C7
LCSG ▷ C9×C17
UCSC1 ◁ C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 71);