Finite Group Databasebeta

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C5×C17⋊(D29⋊C7) #46828519

order34510
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17⋊(D29⋊C7)
unambiguous semidirect productC17⋊(C5×D29⋊C7)
unambiguous semidirect product(C29⋊C7)⋊(C5×D17)
unambiguous semidirect productD493⋊(C5×C7)
unambiguous semidirect product(C5×D493)⋊C7

Splittings

Fitting, socle, HallC5×C17×C29 ⋊ C2×C7
derived, HallC17×C29 ⋊ C2×C5×C7
HallC5×C17×C29⋊C7 ⋊ C2
HallC5×D493 ⋊ C7
HallC17×C29⋊C7 ⋊ C2×C5
HallC5×C29⋊C7 ⋊ D17
HallD493 ⋊ C5×C7
HallC29⋊C7 ⋊ C5×D17
HallC5×C29 ⋊ C7×D17
HallC5×C17 ⋊ D29⋊C7
SylowC29 ⋊ C5×C7×D17
SylowC17 ⋊ C5×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC5C17⋊(D29⋊C7)
commutator, cosocle, hypocenterC17×C29C2×C5×C7
FrattiniC1G
Fitting, socleC5×C17×C29C2×C7
LCSG ▷ C17×C29
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2465

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 20);