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AGL(1,𝔽7)×(C31⋊C3)⋊C5 #34086170

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productAGL(1,𝔽7)×(C31⋊C3)⋊C5
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×(C31⋊C3)⋊C5)
unambiguous semidirect product(AGL(1,𝔽7)×C31⋊C3)⋊C5
unambiguous semidirect product(D7×(C31⋊C3)⋊C5)⋊C3
unambiguous semidirect product(AGL(1,𝔽7)×ΓL(1,𝔽32))⋊C3
unambiguous semidirect product(#13049959⋊C5)⋊C3
unambiguous semidirect product(#13049958⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC7×C31 ⋊ C2×C32×C5
HallΓL(1,𝔽8)×(C31⋊C3)⋊C5 ⋊ C2
HallAGL(1,𝔽7)×C31⋊C3 ⋊ C5
HallD7×ΓL(1,𝔽32) ⋊ C32
HallΓL(1,𝔽8)×C31⋊C3 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C32
HallD7×C31 ⋊ C32×C5
HallΓL(1,𝔽32) ⋊ C3×AGL(1,𝔽7)
SylowC31 ⋊ C3×C5×AGL(1,𝔽7)
HallD7 ⋊ C3×(C31⋊C3)⋊C5
SylowC7 ⋊ C2×C3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C31C2×C32×C5
LCSG ▷ C7×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 217

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 75);