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C2×C3×AGL(1,𝔽31) #19150100

order5580
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(D31⋊C5)⋊(C2×C32)
unambiguous semidirect product(C2×D31⋊C3)⋊(C3×C5)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C22×C3)
unambiguous semidirect product(C2×D31⋊C5)⋊C32
unambiguous semidirect product(C2×(C31⋊C3)⋊C5)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D31⋊C3)⋊C5
unambiguous semidirect product(C2×C3×D31⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C31 ⋊ C2×C3×C5
derived, SylowC31 ⋊ C22×C32×C5
HallC3×(C31⋊C3)⋊C5 ⋊ C22
HallC2×C3×D31⋊C3 ⋊ C5
HallC2×D31⋊C5 ⋊ C32
HallC3×C31⋊C3 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C22×C32
HallC2×D31 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽31)
commutator, hypocenterC31C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×AGL(1,𝔽31), C2×C3×C5×AGL(1,𝔽31), C2×C3×C5⋊AGL(1,𝔽31), …
maximal normal subgroup ofC2×C3×C5×AGL(1,𝔽31), C2×D3×AGL(1,𝔽31), C3×C4×AGL(1,𝔽31), …
maximal quotient ofC2×C3×(D31⋊C3)⋊C25, C3×D5×AGL(1,𝔽31), C2×C3×C5×AGL(1,𝔽31), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 89);