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D3×C17×C41⋊C5 #35229983

order20910
automorphism?
homologyAbelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productD3×C17×C41⋊C5
unambiguous semidirect productC3⋊(C2×C17×C41⋊C5)
unambiguous semidirect product(D3×C41)⋊(C5×C17)
unambiguous semidirect product(D3×C17×C41)⋊C5

Splittings

Fitting, socle, HallC3×C17×C41 ⋊ C2×C5
derived, HallC3×C41 ⋊ C2×C5×C17
HallC3×C17×C41⋊C5 ⋊ C2
HallD3×C17×C41 ⋊ C5
HallC17×C41 ⋊ C5×D3
HallC3×C41⋊C5 ⋊ C2×C17
HallD3×C41 ⋊ C5×C17
HallC3×C17 ⋊ C2×C41⋊C5
SylowC41 ⋊ C5×D3×C17
SylowC3 ⋊ C2×C17×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC17D3×C41⋊C5
commutator, cosocle, hypocenterC3×C41C2×C5×C17
FrattiniC1G
Fitting, socleC3×C17×C41C2×C5
LCSG ▷ C3×C41
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2091

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20910, 21);