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C7×D45⋊D17 #36339266

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

Aliases

direct productC7×D45⋊D17
unambiguous semidirect productD45⋊(C7×D17)
unambiguous semidirect productD85⋊(C7×D9)
unambiguous semidirect productD153⋊(C7×D5)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C22
derived, HallC5×C9×C17 ⋊ C22×C7
HallC7×C9×C17 ⋊ C2×D5
HallC5×C7×C17 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D17
HallC9×C17 ⋊ C2×C7×D5
HallC7×C17 ⋊ D5×D9
HallC5×C17 ⋊ C2×C7×D9
HallC7×C9 ⋊ D5×D17
HallC5×C9 ⋊ C2×C7×D17
HallC5×C7 ⋊ D9×D17
SylowC17 ⋊ C7×D5×D9
SylowC9 ⋊ C7×D5×D17
SylowC5 ⋊ C7×D9×D17

Subgroups

subgroupG/H
center, hypercenterC7D45⋊D17
commutator, cosocle, hypocenterC5×C9×C17C22×C7
FrattiniC3C7×D15⋊D17
FittingC5×C7×C9×C17C22
socleC3×C5×C7×C17C2×D3
LCSG ▷ C5×C9×C17
UCSC1 ◁ C7

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 98);