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C7×C3⋊D3×ΓL(1,𝔽32) #34086220

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

Aliases

direct productC7×C3⋊D3×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(D3×C7×ΓL(1,𝔽32))
unambiguous semidirect product(C3⋊D3×C31)⋊(C5×C7)
unambiguous semidirect product(C7×C3⋊D3×C31)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7C3⋊D3×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC32×C31C2×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C31C2×C5
LCSG ▷ C32×C31
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1953

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 125);