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(#16811774⋊C2)⋊C3 #35205679

order20460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(#16811774⋊C2)⋊C3
unambiguous semidirect product(#16811774⋊C3)⋊C2
unambiguous semidirect product(#16811780⋊C3)⋊C2
unambiguous semidirect product(#16811786⋊C3)⋊C2

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C22×C3×C5
Hall#16811774⋊C2 ⋊ C3
Hall#13133724⋊C3 ⋊ C22
HallD11×D31⋊C3 ⋊ C5
Hall#13133724 ⋊ C22×C3
HallD11×D31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C22×C5
HallC31⋊C3 ⋊ C2×AGL(1,𝔽11)
SylowC31 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C31C22×C3×C5
LCSG ▷ C11×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 341

Polycyclic presentation:

2^2,3,5,11,31|f^a=f^30,e^b=e^10,f^c=f^5,e^d=e^4,f^d=f^2

Conjugacy classes & character table

73 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 99);