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C13⋊C3×AGL(1,𝔽31) #49136556

order36270
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC13⋊C3×AGL(1,𝔽31)
unambiguous semidirect product(D31⋊C3)⋊(C5×C13⋊C3)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C2×C13⋊C3)
unambiguous semidirect product(C13⋊C3×D31⋊C3)⋊C5
unambiguous semidirect product(C13×AGL(1,𝔽31))⋊C3
unambiguous semidirect product(C13⋊C3×D31⋊C5)⋊C3
unambiguous semidirect product(#14559022⋊C5)⋊C3
unambiguous semidirect product(#14559023⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2×C32×C5
HallC13⋊C3×(C31⋊C3)⋊C5 ⋊ C2
HallC13⋊C3×D31⋊C3 ⋊ C5
HallC13×D31⋊C5 ⋊ C32
HallC13⋊C3×C31⋊C3 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C32
HallC13×D31 ⋊ C32×C5
HallD31⋊C5 ⋊ C3×C13⋊C3
HallΓL(1,𝔽32) ⋊ C2×C3×C13⋊C3
HallD31 ⋊ C3×C5×C13⋊C3
SylowC31 ⋊ C2×C3×C5×C13⋊C3
SylowC13 ⋊ C3×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C31C2×C32×C5
LCSG ▷ C13×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 403

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 76);