Finite Group Databasebeta

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C29×D595 #46828515

order34510
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D595
unambiguous semidirect productC5⋊(C29×D119)
unambiguous semidirect productC7⋊(C29×D85)
unambiguous semidirect productC17⋊(C29×D35)

Splittings

Fitting, socle, HallC5×C7×C17×C29 ⋊ C2
derived, HallC5×C7×C17 ⋊ C2×C29
HallC7×C17×C29 ⋊ D5
HallC5×C17×C29 ⋊ D7
HallC5×C7×C29 ⋊ D17
HallC17×C29 ⋊ D35
HallC7×C29 ⋊ D85
HallC5×C29 ⋊ D119
HallC7×C17 ⋊ D5×C29
HallC5×C17 ⋊ D7×C29
HallC5×C7 ⋊ C29×D17
SylowC17 ⋊ C29×D35
SylowC7 ⋊ C29×D85
SylowC5 ⋊ C29×D119

Subgroups

subgroupG/H
center, hypercenterC29D595
commutator, cosocle, hypocenterC5×C7×C17C2×C29
FrattiniC1G
Fitting, socleC5×C7×C17×C29C2
LCSG ▷ C5×C7×C17
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17255

Conjugacy classes & character table

8671 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 16);