Finite Group Databasebeta

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C5×C7×C29×D17 #46828503

order34510
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C29×D17
unambiguous semidirect productC17⋊(C2×C5×C7×C29)

Splittings

Fitting, socle, HallC5×C7×C17×C29 ⋊ C2
derived, SylowC17 ⋊ C2×C5×C7×C29
HallC7×C17×C29 ⋊ C2×C5
HallC5×C17×C29 ⋊ C2×C7
HallC5×C7×C17 ⋊ C2×C29
HallC17×C29 ⋊ C2×C5×C7
HallC7×C17 ⋊ C2×C5×C29
HallC5×C17 ⋊ C2×C7×C29

Subgroups

subgroupG/H
center, hypercenterC5×C7×C29D17
commutator, cosocle, hypocenterC17C2×C5×C7×C29
FrattiniC1G
Fitting, socleC5×C7×C17×C29C2
LCSG ▷ C17
UCSC1 ◁ C5×C7×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17255

Conjugacy classes & character table

10150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 4);