Finite Group Databasebeta

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D17×D525 #49087616

order35700
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD17×D525
unambiguous semidirect product(C3×D17)⋊D175
unambiguous semidirect product(C7×D17)⋊D75
unambiguous semidirect product(C25×D17)⋊D21

Splittings

Fitting, derived, HallC3×C7×C17×C25 ⋊ C22
HallC7×C17×C25 ⋊ C2×D3
HallC3×C17×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C2×D17
HallC17×C25 ⋊ C2×D21
HallC3×C7×C17 ⋊ C2×D25
HallC7×C25 ⋊ D3×D17
HallC7×C17 ⋊ C2×D75
HallC3×C25 ⋊ D7×D17
HallC3×C17 ⋊ C2×D175
SylowC25 ⋊ D17×D21
HallC3×C7 ⋊ D17×D25
SylowC17 ⋊ C2×D525
SylowC7 ⋊ D17×D75
SylowC3 ⋊ D17×D175

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C7×C17×C25C22
FrattiniC5D17×D105
socleC3×C5×C7×C17C2×D5
LCSG ▷ C3×C7×C17×C25
UCSC1

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) = 8925

Conjugacy classes & character table

2640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 90);