Finite Group Databasebeta

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D85×C29⋊C7 #46828522

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

Aliases

direct productD85×C29⋊C7
unambiguous semidirect productC5⋊(D17×C29⋊C7)
unambiguous semidirect productC17⋊(D5×C29⋊C7)
unambiguous semidirect product(C29×D85)⋊C7

Splittings

Fitting, socle, derived, HallC5×C17×C29 ⋊ C2×C7
HallC5×C17×C29⋊C7 ⋊ C2
HallC29×D85 ⋊ C7
HallC17×C29⋊C7 ⋊ D5
HallC5×C29⋊C7 ⋊ D17
HallC17×C29 ⋊ C7×D5
HallC5×C29 ⋊ C7×D17
HallC5×C17 ⋊ C2×C29⋊C7
SylowC29 ⋊ C7×D85
SylowC17 ⋊ D5×C29⋊C7
SylowC5 ⋊ D17×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C17×C29C2×C7
LCSG ▷ C5×C17×C29
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2465

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 23);