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C3×C5⋊AGL(1,𝔽31) #28358448

order13950
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊AGL(1,𝔽31)
unambiguous semidirect productC5⋊(C3×AGL(1,𝔽31))
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C3×D5)
unambiguous semidirect product(C5⋊(D31⋊C3))⋊(C3×C5)
unambiguous semidirect product(C5⋊(D31⋊C5))⋊C32
unambiguous semidirect product(C3×C5⋊(D31⋊C3))⋊C5
unambiguous semidirect product(C3×C5⋊(D31⋊C5))⋊C3

Splittings

Fitting, socleC3×C5×C31 ⋊ C2×C3×C5
derivedC5×C31 ⋊ C2×C32×C5
HallC3×C5×(C31⋊C3)⋊C5 ⋊ C2
HallC5⋊(D31⋊C5) ⋊ C32
HallC5×ΓL(1,𝔽32) ⋊ C2×C32
HallC3×C31⋊C3 ⋊ C5×D5
SylowC31 ⋊ C32×C5×D5

Subgroups

subgroupG/H
center, hypercenterC3C5⋊AGL(1,𝔽31)
commutator, cosocle, hypocenterC5×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C31C2×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×AGL(1,𝔽31), D3×C5⋊AGL(1,𝔽31), D15⋊AGL(1,𝔽31), …
maximal normal subgroup ofC3×D5×AGL(1,𝔽31), D3×C5⋊AGL(1,𝔽31), D15⋊AGL(1,𝔽31), …
maximal quotient ofC3×((C31⋊C3)⋊C5)⋊Dic5, C2×C3×C5⋊AGL(1,𝔽31)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 91);