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AGL(1,𝔽11)×D31⋊C3 #35205682

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

Aliases

direct productAGL(1,𝔽11)×D31⋊C3
unambiguous semidirect productD11⋊(C5×D31⋊C3)
unambiguous semidirect product(D31×AGL(1,𝔽11))⋊C3
unambiguous semidirect product(C11⋊C5×D31⋊C3)⋊C2
unambiguous semidirect product(C31⋊C3×AGL(1,𝔽11))⋊C2
unambiguous semidirect product((C11⋊C5)⋊(D31⋊C3))⋊C2

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C22×C3×C5
HallD31×AGL(1,𝔽11) ⋊ C3
HallC11⋊C5×C31⋊C3 ⋊ C22
HallD11×D31⋊C3 ⋊ C5
HallC31×C11⋊C5 ⋊ C22×C3
HallD11×D31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C22×C5
HallC31⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D31⋊C3
SylowC31 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D31⋊C3

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

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 102);