Finite Group Databasebeta

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C3×C17×D29⋊C7 #35208487

order20706
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×D29⋊C7
unambiguous semidirect productD29⋊(C3×C7×C17)
unambiguous semidirect product(C3×D29)⋊(C7×C17)
unambiguous semidirect product(C29⋊C7)⋊(C2×C3×C17)
unambiguous semidirect product(C17×D29)⋊(C3×C7)
unambiguous semidirect product(C3×C17×D29)⋊C7

Splittings

Fitting, socle, HallC3×C17×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C2×C3×C7×C17
HallC3×C17×C29⋊C7 ⋊ C2
HallC17×C29⋊C7 ⋊ C2×C3
HallC3×C17×D29 ⋊ C7
HallC17×D29 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ C2×C17
HallC17×C29 ⋊ C2×C3×C7
HallC29⋊C7 ⋊ C2×C3×C17
HallC3×D29 ⋊ C7×C17
HallC3×C29 ⋊ C2×C7×C17
HallD29 ⋊ C3×C7×C17

Subgroups

subgroupG/H
center, hypercenterC3×C17D29⋊C7
commutator, cosocle, hypocenterC29C2×C3×C7×C17
FrattiniC1G
Fitting, socleC3×C17×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1479

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20706, 19);