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D63×ΓL(1,𝔽32) #34086126

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

Aliases

direct productD63×ΓL(1,𝔽32)
unambiguous semidirect productC7⋊(D9×ΓL(1,𝔽32))
unambiguous semidirect productC9⋊(D7×ΓL(1,𝔽32))
unambiguous semidirect product(C31×D63)⋊C5

Splittings

Fitting, derived, HallC7×C9×C31 ⋊ C2×C5
HallC7×C9×ΓL(1,𝔽32) ⋊ C2
HallC31×D63 ⋊ C5
HallC9×ΓL(1,𝔽32) ⋊ D7
HallC7×ΓL(1,𝔽32) ⋊ D9
HallC9×C31 ⋊ C5×D7
HallC7×C31 ⋊ C5×D9
HallC7×C9 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D63
SylowC9 ⋊ D7×ΓL(1,𝔽32)
SylowC7 ⋊ D9×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC7×C9×C31C2×C5
FrattiniC3D21×ΓL(1,𝔽32)
socleC3×C7×C31C5×D3
LCSG ▷ C7×C9×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1953

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 31);