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C7×D9×ΓL(1,𝔽32) #34086124

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

Aliases

direct productC7×D9×ΓL(1,𝔽32)
unambiguous semidirect productC9⋊(C2×C7×ΓL(1,𝔽32))
unambiguous semidirect product(D9×C31)⋊(C5×C7)
unambiguous semidirect product(C7×D9×C31)⋊C5

Splittings

Fitting, HallC7×C9×C31 ⋊ C2×C5
derived, HallC9×C31 ⋊ C2×C5×C7
HallC7×C9×ΓL(1,𝔽32) ⋊ C2
HallC7×D9×C31 ⋊ C5
HallC9×ΓL(1,𝔽32) ⋊ C2×C7
HallD9×C31 ⋊ C5×C7
HallC7×C31 ⋊ C5×D9
HallC7×C9 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C7×D9
SylowC9 ⋊ C2×C7×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC7D9×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC9×C31C2×C5×C7
FrattiniC3D3×C7×ΓL(1,𝔽32)
FittingC7×C9×C31C2×C5
socleC3×C7×C31C5×D3
LCSG ▷ C9×C31
UCSC1 ◁ C7

48 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, 29);