Finite Group Databasebeta

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C2×C5×C7×C9×D17 #36339296

order21420
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×C9×D17
unambiguous semidirect productC17⋊(C22×C5×C7×C9)
unambiguous semidirect product(C2×C17)⋊(C2×C5×C7×C9)

Splittings

FittingC2×C5×C7×C9×C17 ⋊ C2
derived, SylowC17 ⋊ C22×C5×C7×C9
HallC5×C7×C9×C17 ⋊ C22
HallC7×C9×C17 ⋊ C22×C5
HallC5×C9×C17 ⋊ C22×C7
HallC5×C7×C17 ⋊ C22×C9
HallC9×C17 ⋊ C22×C5×C7
HallC7×C17 ⋊ C22×C5×C9
HallC5×C17 ⋊ C22×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C9D17
commutator, hypocenterC17C22×C5×C7×C9
FrattiniC3C2×C3×C5×C7×D17
FittingC2×C5×C7×C9×C17C2
socleC2×C3×C5×C7×C17C2×C3
prime radicalC2×C3×C5×C7×D17C3
cosocleC3×C17C22×C3×C5×C7
LCSG ▷ C17
UCSC1 ◁ C2×C5×C7×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10710

Conjugacy classes & character table

6300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 128);