Finite Group Databasebeta

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C52×D17×D21 #49087924

order35700
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×D17×D21
unambiguous semidirect product(C3×D17)⋊(C52×D7)
unambiguous semidirect product(C7×D17)⋊(C52×D3)

Splittings

Fitting, socle, HallC3×C52×C7×C17 ⋊ C22
derived, HallC3×C7×C17 ⋊ C22×C52
HallC52×C7×C17 ⋊ C2×D3
HallC3×C52×C17 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D17
HallC52×C17 ⋊ C2×D21
HallC52×C7 ⋊ D3×D17
HallC7×C17 ⋊ C2×C52×D3
HallC3×C52 ⋊ D7×D17
HallC3×C17 ⋊ C2×C52×D7
HallC3×C7 ⋊ C2×C52×D17
SylowC17 ⋊ C2×C52×D21
SylowC7 ⋊ C52×D3×D17
SylowC3 ⋊ C52×D7×D17

Subgroups

subgroupG/H
center, hypercenterC52D17×D21
commutator, cosocle, hypocenterC3×C7×C17C22×C52
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C7×C17
UCSC1 ◁ C52

320 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 128 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

3000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 398);