Finite Group Databasebeta

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C5×D3×C17×D29 #44443842

order29580
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×C17×D29
unambiguous semidirect product(D3×C29)⋊(C2×C5×C17)
unambiguous semidirect product(C3×D29)⋊(C2×C5×C17)
unambiguous semidirect productD87⋊(C2×C5×C17)

Splittings

Fitting, socle, HallC3×C5×C17×C29 ⋊ C22
derived, HallC3×C29 ⋊ C22×C5×C17
HallC5×C17×C29 ⋊ C2×D3
HallC3×C17×C29 ⋊ C22×C5
HallC17×C29 ⋊ C2×C5×D3
HallC3×C5×C29 ⋊ C22×C17
HallC3×C5×C17 ⋊ C2×D29
HallC5×C29 ⋊ C2×D3×C17
HallC3×C17 ⋊ C2×C5×D29
SylowC29 ⋊ C2×C5×D3×C17
HallC3×C5 ⋊ C2×C17×D29
SylowC3 ⋊ C2×C5×C17×D29

Subgroups

subgroupG/H
center, hypercenterC5×C17D3×D29
commutator, cosocle, hypocenterC3×C29C22×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C29C22
LCSG ▷ C3×C29
UCSC1 ◁ C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7395

Conjugacy classes & character table

4080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29580, 54);