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C3⋊AGL(1,𝔽7)×ΓL(1,𝔽32) #34086192

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

Aliases

direct productC3⋊AGL(1,𝔽7)×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(AGL(1,𝔽7)×ΓL(1,𝔽32))
unambiguous semidirect productΓL(1,𝔽8)⋊(D3×ΓL(1,𝔽32))
unambiguous semidirect productD21⋊(C3×ΓL(1,𝔽32))
unambiguous semidirect product(C31×C3⋊AGL(1,𝔽7))⋊C5

Splittings

Fitting, socle, derivedC3×C7×C31 ⋊ C2×C3×C5
HallC3×ΓL(1,𝔽8)×ΓL(1,𝔽32) ⋊ C2
HallC31×C3⋊AGL(1,𝔽7) ⋊ C5
HallC3×ΓL(1,𝔽8)×C31 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C3×D3
HallC7×C31 ⋊ C3×C5×D3
HallC3×ΓL(1,𝔽8) ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C3⋊AGL(1,𝔽7)
SylowC7 ⋊ C3×D3×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C31C2×C3×C5
LCSG ▷ C3×C7×C31
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 651

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 97);