Finite Group Databasebeta

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C3×D31×AGL(1,𝔽11) #35205706

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

Aliases

direct productC3×D31×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×D31)

Splittings

Fitting, socle, HallC3×C11×C31 ⋊ C22×C5
derived, HallC11×C31 ⋊ C22×C3×C5
HallC3×C31×C11⋊C5 ⋊ C22
HallC3×D11×D31 ⋊ C5
HallC31×C11⋊C5 ⋊ C22×C3
HallD11×D31 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ C2×D31
HallC3×C31 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×C3×D31
HallC3×C11 ⋊ C2×C5×D31
SylowC31 ⋊ C2×C3×AGL(1,𝔽11)
SylowC11 ⋊ C2×C3×C5×D31

Subgroups

subgroupG/H
center, hypercenterC3D31×AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C31C22×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C31C22×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 126);