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C5×D3×D71⋊C7 #44447175

order29820
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×D71⋊C7
unambiguous semidirect product(C5×D3×D71)⋊C7

Splittings

Fitting, socle, HallC3×C5×C71 ⋊ C22×C7
derived, HallC3×C71 ⋊ C22×C5×C7
HallC3×C5×C71⋊C7 ⋊ C22
HallC5×D3×D71 ⋊ C7
HallC5×C71⋊C7 ⋊ C2×D3
HallC3×C71⋊C7 ⋊ C22×C5
HallD3×D71 ⋊ C5×C7
HallC71⋊C7 ⋊ C2×C5×D3
HallC5×C71 ⋊ C2×D3×C7
SylowC71 ⋊ C2×C5×D3×C7
HallC3×C5 ⋊ C2×D71⋊C7
SylowC3 ⋊ C2×C5×D71⋊C7

Subgroups

subgroupG/H
center, hypercenterC5D3×D71⋊C7
commutator, cosocle, hypocenterC3×C71C22×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C71C22×C7
LCSG ▷ C3×C71
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1065

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 63);