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C17⋊((D61⋊C3)⋊C5) #44527463

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

Aliases

unambiguous semidirect productC17⋊((D61⋊C3)⋊C5)
unambiguous semidirect product((C61⋊C3)⋊C5)⋊D17
unambiguous semidirect product(C17⋊(D61⋊C3))⋊C5
unambiguous semidirect product(C17⋊(D61⋊C5))⋊C3

Splittings

Fitting, socle, derived, HallC17×C61 ⋊ C2×C3×C5
HallC17×(C61⋊C3)⋊C5 ⋊ C2
HallC17⋊(D61⋊C5) ⋊ C3
HallC17⋊(D61⋊C3) ⋊ C5
HallC17×C61⋊C5 ⋊ C2×C3
HallC17×C61⋊C3 ⋊ C2×C5
HallD1037 ⋊ C3×C5
Hall(C61⋊C3)⋊C5 ⋊ D17
HallC61⋊C5 ⋊ C3×D17
HallC61⋊C3 ⋊ C5×D17
SylowC61 ⋊ C3×C5×D17
SylowC17 ⋊ (D61⋊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

Polycyclic presentation:

2,3,5,17,61|d^a=d^16,e^a=e^60,e^b=e^47,e^c=e^9

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 36);