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D3×C13×ΓL(1,𝔽32) #27130657

order12090
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productD3×C13×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C2×C13×ΓL(1,𝔽32))
unambiguous semidirect product(D3×C31)⋊(C5×C13)
unambiguous semidirect product(D3×C13×C31)⋊C5

Splittings

Fitting, socle, HallC3×C13×C31 ⋊ C2×C5
derived, HallC3×C31 ⋊ C2×C5×C13
HallC3×C13×ΓL(1,𝔽32) ⋊ C2
HallD3×C13×C31 ⋊ C5
HallC3×ΓL(1,𝔽32) ⋊ C2×C13
HallC13×C31 ⋊ C5×D3
HallD3×C31 ⋊ C5×C13
HallC3×C13 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D3×C13
SylowC3 ⋊ C2×C13×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC13D3×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC3×C31C2×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

429 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C13×D31⋊C5, D3×C13⋊(D31⋊C5), D3×D13×ΓL(1,𝔽32), …
maximal normal subgroup ofD3×C13×D31⋊C5, D3×C13⋊(D31⋊C5), D3×D13×ΓL(1,𝔽32), …
maximal quotient ofDic3×C13×ΓL(1,𝔽32), C2×D3×C13×ΓL(1,𝔽32), C13×D9×ΓL(1,𝔽32), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 29);