Finite Group Databasebeta

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C3×C5×C31×AGL(1,𝔽7) #34086225

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C31 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C31×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C32×C5×C31)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C3×C5×C31)
unambiguous semidirect product(C3×D7)⋊(C3×C5×C31)
unambiguous semidirect product(C5×D7)⋊(C32×C31)
unambiguous semidirect product(C3×C5×D7)⋊(C3×C31)

Splittings

Fitting, socleC3×C5×C7×C31 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C32×C5×C31
HallC3×C5×ΓL(1,𝔽8)×C31 ⋊ C2
HallC5×D7×C31 ⋊ C32
HallC3×ΓL(1,𝔽8)×C31 ⋊ C2×C5
HallC5×C7×C31 ⋊ C2×C32
HallD7×C31 ⋊ C32×C5
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C31
HallC7×C31 ⋊ C2×C32×C5
HallC5×D7 ⋊ C32×C31
HallC3×ΓL(1,𝔽8) ⋊ C2×C5×C31
HallC5×C7 ⋊ C2×C32×C31
HallD7 ⋊ C32×C5×C31

Subgroups

subgroupG/H
center, hypercenterC3×C5×C31AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C32×C5×C31
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C31

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3255

Conjugacy classes & character table

3255 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 130);