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C5×ΓL(1,𝔽8)⋊(D31⋊C3) #34086201

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

Aliases

direct productC5×ΓL(1,𝔽8)⋊(D31⋊C3)
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D31⋊C3)
unambiguous semidirect product(C5×(C31⋊C3)⋊D7)⋊C3
unambiguous semidirect product(C5×ΓL(1,𝔽8)⋊D31)⋊C3
unambiguous semidirect product(C5×#13049961)⋊C3
unambiguous semidirect product(C5×#13049960)⋊C3

Splittings

Fitting, socle, HallC5×C7×C31 ⋊ C2×C32
derived, HallC7×C31 ⋊ C2×C32×C5
HallC5×ΓL(1,𝔽8)×C31⋊C3 ⋊ C2
HallC5×D217 ⋊ C32
HallΓL(1,𝔽8)×C31⋊C3 ⋊ C2×C5
HallD217 ⋊ C32×C5
HallC5×C31 ⋊ C3×AGL(1,𝔽7)
HallC5×C7 ⋊ C3×D31⋊C3
SylowC31 ⋊ C3×C5×AGL(1,𝔽7)
SylowC7 ⋊ C3×C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊(D31⋊C3)
commutator, cosocle, hypocenterC7×C31C2×C32×C5
FrattiniC1G
Fitting, socleC5×C7×C31C2×C32
LCSG ▷ C7×C31
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1085

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 106);