Finite Group Databasebeta

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C2×C5×C17×C29⋊C7 #46828501

order34510
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C17×C29⋊C7
unambiguous semidirect product(C2×C29)⋊(C5×C7×C17)
unambiguous semidirect product(C2×C5×C29)⋊(C7×C17)
unambiguous semidirect product(C2×C17×C29)⋊(C5×C7)
unambiguous semidirect product(C2×C5×C17×C29)⋊C7

Splittings

Fitting, socle, HallC2×C5×C17×C29 ⋊ C7
derived, SylowC29 ⋊ C2×C5×C7×C17
HallC5×C17×C29 ⋊ C2×C7
HallC2×C17×C29 ⋊ C5×C7
HallC17×C29 ⋊ C2×C5×C7
HallC2×C5×C29 ⋊ C7×C17
HallC5×C29 ⋊ C2×C7×C17
HallC2×C29 ⋊ C5×C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17C29⋊C7
commutator, cosocle, hypocenterC29C2×C5×C7×C17
FrattiniC1G
Fitting, socleC2×C5×C17×C29C7
LCSG ▷ C29
UCSC1 ◁ C2×C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4930

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 2);