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D17×(C61⋊C3)⋊C5 #44527462

order31110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD17×(C61⋊C3)⋊C5
unambiguous semidirect productC17⋊(C2×(C61⋊C3)⋊C5)
unambiguous semidirect product(D17×C61⋊C3)⋊C5
unambiguous semidirect product(D17×C61⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC17×C61 ⋊ C2×C3×C5
HallC17×(C61⋊C3)⋊C5 ⋊ C2
HallD17×C61⋊C5 ⋊ C3
HallD17×C61⋊C3 ⋊ C5
HallC17×C61⋊C5 ⋊ C2×C3
HallC17×C61⋊C3 ⋊ C2×C5
HallD17×C61 ⋊ C3×C5
HallC61⋊C5 ⋊ C3×D17
HallC61⋊C3 ⋊ C5×D17
SylowC61 ⋊ C3×C5×D17
SylowC17 ⋊ C2×(C61⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC17×C61C2×C3×C5
LCSG ▷ C17×C61
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1037

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 35);