Finite Group Databasebeta

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C3×D17×C29⋊C7 #35208488

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

Aliases

direct productC3×D17×C29⋊C7
unambiguous semidirect productC17⋊(C2×C3×C29⋊C7)
unambiguous semidirect product(C29×D17)⋊(C3×C7)
unambiguous semidirect product(C3×C29×D17)⋊C7

Splittings

Fitting, socle, HallC3×C17×C29 ⋊ C2×C7
derived, HallC17×C29 ⋊ C2×C3×C7
HallC3×C17×C29⋊C7 ⋊ C2
HallC17×C29⋊C7 ⋊ C2×C3
HallC3×C29×D17 ⋊ C7
HallC29×D17 ⋊ C3×C7
HallC3×C29 ⋊ C7×D17
HallC3×C17 ⋊ C2×C29⋊C7
SylowC29 ⋊ C3×C7×D17
SylowC17 ⋊ C2×C3×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC3D17×C29⋊C7
commutator, cosocle, hypocenterC17×C29C2×C3×C7
FrattiniC1G
Fitting, socleC3×C17×C29C2×C7
LCSG ▷ C17×C29
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1479

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20706, 20);