Finite Group Databasebeta

← Prev (#34086215) Next (#34086217) →

C3×D3×C7×ΓL(1,𝔽32) #34086216

order19530
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3×C7×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C2×C3×C7×ΓL(1,𝔽32))
unambiguous semidirect product(C3×D3×C31)⋊(C5×C7)
unambiguous semidirect product(C3×D3×C7×C31)⋊C5

Splittings

Fitting, socle, HallC32×C7×C31 ⋊ C2×C5
derivedC3×C31 ⋊ C2×C3×C5×C7
HallC32×C7×ΓL(1,𝔽32) ⋊ C2
HallC3×D3×C7×C31 ⋊ C5
HallC32×ΓL(1,𝔽32) ⋊ C2×C7
HallC3×D3×C31 ⋊ C5×C7
HallC32×C31 ⋊ C2×C5×C7
HallC7×C31 ⋊ C3×C5×D3
HallC32×C7 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C3×C5×D3×C7
SylowC32 ⋊ C2×C7×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3×C7D3×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC3×C31C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1302

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 121);