Finite Group Databasebeta

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D3×C11×D31⋊C5 #35205708

order20460
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11×D31⋊C5
unambiguous semidirect productD31⋊(C5×D3×C11)
unambiguous semidirect product(D3×D31)⋊(C5×C11)
unambiguous semidirect product(C3×D31⋊C5)⋊(C2×C11)
unambiguous semidirect product(D3×ΓL(1,𝔽32))⋊(C2×C11)
unambiguous semidirect product(C3⋊(D31⋊C5))⋊(C2×C11)

Splittings

Fitting, socle, HallC3×C11×C31 ⋊ C22×C5
derived, HallC3×C31 ⋊ C22×C5×C11
HallC3×C11×ΓL(1,𝔽32) ⋊ C22
HallD3×C11×D31 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×ΓL(1,𝔽32) ⋊ C22×C11
HallD3×D31 ⋊ C5×C11
HallC11×C31 ⋊ C2×C5×D3
HallΓL(1,𝔽32) ⋊ C2×D3×C11
HallC3×C11 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×D3×C11
SylowC3 ⋊ C2×C11×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC11D3×D31⋊C5
commutator, cosocle, hypocenterC3×C31C22×C5×C11
FrattiniC1G
Fitting, socleC3×C11×C31C22×C5
LCSG ▷ C3×C31
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 128);