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C3×C5×AGL(1,𝔽31) #28358447

order13950
automorphism?
homologyAbelianization (H1) = C2×C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C5×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C3×C52)
unambiguous semidirect product(D31⋊C5)⋊(C32×C5)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C2×C3×C5)
unambiguous semidirect product(C3×D31⋊C3)⋊C52
unambiguous semidirect product(C3×D31⋊C5)⋊(C3×C5)
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
derived, SylowC31 ⋊ C2×C32×C52
HallC3×C5×(C31⋊C3)⋊C5 ⋊ C2
HallC5×D31⋊C5 ⋊ C32
HallC5×ΓL(1,𝔽32) ⋊ C2×C32
HallC3×D31⋊C3 ⋊ C52
HallC3×C31⋊C3 ⋊ C2×C52
HallD31 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC3×C5AGL(1,𝔽31)
commutator, cosocle, hypocenterC31C2×C32×C52
FrattiniC1G
Fitting, socleC3×C5×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C3×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

465 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×AGL(1,𝔽31), C5×D3×AGL(1,𝔽31), D15×AGL(1,𝔽31), …
maximal normal subgroup ofC3×D5×AGL(1,𝔽31), C5×D3×AGL(1,𝔽31), D15×AGL(1,𝔽31), …
maximal quotient ofC3×C5×((C31⋊C3)⋊C4)⋊C5, C2×C3×C5×AGL(1,𝔽31)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 90);