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D17×AGL(1,𝔽31) #44539283

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productD17×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C5×D17)
unambiguous semidirect product(D31⋊C5)⋊(C3×D17)
unambiguous semidirect product(D17×D31⋊C3)⋊C5
unambiguous semidirect product(D17×D31⋊C5)⋊C3
unambiguous semidirect product(C17×AGL(1,𝔽31))⋊C2
unambiguous semidirect product(D17×(C31⋊C3)⋊C5)⋊C2
unambiguous semidirect product(C17⋊AGL(1,𝔽31))⋊C2

Splittings

Fitting, socle, derived, HallC17×C31 ⋊ C22×C3×C5
HallD17×D31⋊C5 ⋊ C3
HallC17×(C31⋊C3)⋊C5 ⋊ C22
HallD17×D31⋊C3 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C22×C3
HallD17×D31 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C22×C5
Hall(C31⋊C3)⋊C5 ⋊ C2×D17
HallΓL(1,𝔽32) ⋊ C2×C3×D17
HallC31⋊C3 ⋊ C2×C5×D17
SylowC31 ⋊ C2×C3×C5×D17
SylowC17 ⋊ C2×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC17×C31C22×C3×C5
LCSG ▷ C17×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 527

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 40);