Finite Group Databasebeta

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C3×D3×C7×D85 #36339478

order21420
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC3×D3×C7×D85
unambiguous semidirect product(C5×D3)⋊(C3×C7×D17)
unambiguous semidirect product(D3×C17)⋊(C3×C7×D5)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C22
derivedC3×C5×C17 ⋊ C22×C3×C7
HallC32×C7×C17 ⋊ C2×D5
HallC32×C5×C17 ⋊ C22×C7
HallC5×C7×C17 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C2×D17
HallC32×C17 ⋊ C2×C7×D5
HallC7×C17 ⋊ C3×D3×D5
HallC5×C17 ⋊ C2×C3×D3×C7
HallC32×C7 ⋊ C2×D85
HallC32×C5 ⋊ C2×C7×D17
HallC5×C7 ⋊ C3×D3×D17
SylowC17 ⋊ C3×D3×C7×D5
SylowC32 ⋊ C2×C7×D85
SylowC5 ⋊ C3×D3×C7×D17

Subgroups

subgroupG/H
center, hypercenterC3×C7D3×D85
commutator, cosocle, hypocenterC3×C5×C17C22×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C3×C5×C17
UCSC1 ◁ C3×C7

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 3570

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 310);