Finite Group Databasebeta

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C7×D5×C17×D9 #36339263

order21420
automorphism?
homologyAbelianization (H1) = C22×C7×C17 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×C17×D9
unambiguous semidirect product(C5×D9)⋊(C2×C7×C17)
unambiguous semidirect product(C9×D5)⋊(C2×C7×C17)
unambiguous semidirect productD45⋊(C2×C7×C17)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C22
derived, HallC5×C9 ⋊ C22×C7×C17
HallC7×C9×C17 ⋊ C2×D5
HallC5×C9×C17 ⋊ C22×C7
HallC5×C7×C17 ⋊ C2×D9
HallC5×C7×C9 ⋊ C22×C17
HallC9×C17 ⋊ C2×C7×D5
HallC5×C17 ⋊ C2×C7×D9
HallC7×C9 ⋊ C2×D5×C17
HallC5×C7 ⋊ C2×C17×D9
SylowC9 ⋊ C2×C7×D5×C17
SylowC5 ⋊ C2×C7×C17×D9

Subgroups

subgroupG/H
center, hypercenterC7×C17D5×D9
commutator, cosocle, hypocenterC5×C9C22×C7×C17
FrattiniC3D3×C7×D5×C17
FittingC5×C7×C9×C17C22
socleC3×C5×C7×C17C2×D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C17

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 5355

Conjugacy classes & character table

2856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 95);