Finite Group Databasebeta

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C5×C7⋊C9×#595 #36339196

order21420
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, HallC7×C17 ⋊ C4×C5×C9
HallC5×C17×C7⋊C9 ⋊ C4
HallC5×C7×#595 ⋊ C9
HallC17×C7⋊C9 ⋊ C4×C5
HallC5×C7×C17 ⋊ C4×C9
HallC7×#595 ⋊ C5×C9
HallC5×C17 ⋊ C4×C7⋊C9
HallC5×C7 ⋊ C9×#595
SylowC17 ⋊ C4×C5×C7⋊C9
SylowC7 ⋊ C5×C9×#595

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)×#595
commutator, hypocenterC7×C17C4×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)×#595
Fitting, socleC3×C5×C7×C17C3×C4
prime radicalC3×C5×C7×D17C2×C3
cosocleC3×C7×D17C2×C3×C5
LCSG ▷ C7×C17
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 28);