Finite Group Databasebeta

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C7×C9×#66772 #36339231

order21420
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×#66772

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C4
derived, HallC5×C17 ⋊ C4×C7×C9
HallC7×C9×C17 ⋊ Dic5
HallC5×C9×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ C4×C9
HallC5×C7×C9 ⋊ #595
HallC9×C17 ⋊ C7×Dic5
HallC7×C17 ⋊ C9×Dic5
HallC5×C9 ⋊ C7×#595
HallC5×C7 ⋊ C9×#595
SylowC17 ⋊ C7×C9×Dic5
SylowC5 ⋊ C7×C9×#595

Subgroups

subgroupG/H
center, hypercenterC7×C9#66772
commutator, hypocenterC5×C17C4×C7×C9
FrattiniC3C3×C7×#66772
FittingC5×C7×C9×C17C4
socleC3×C5×C7×C17C3×C4
prime radicalC3×C5×C7×D17C2×C3
cosocleC3×C5×D17C2×C3×C7
LCSG ▷ C5×C17
UCSC1 ◁ C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 63);