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(C13⋊C3)⋊AGL(1,𝔽31) #49136554

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

Aliases

unambiguous semidirect product(C13⋊C3)⋊AGL(1,𝔽31)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(D13⋊C3)
unambiguous semidirect product((C13⋊C3)⋊(D31⋊C3))⋊C5
unambiguous semidirect product(((C31⋊C3)⋊C5)⋊D13)⋊C3
unambiguous semidirect product((C13⋊C3)⋊(D31⋊C5))⋊C3
unambiguous semidirect product(#14559030⋊C5)⋊C3
unambiguous semidirect product(#14559031⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2×C32×C5
HallC13⋊C3×(C31⋊C3)⋊C5 ⋊ C2
Hall(C13⋊C3)⋊(D31⋊C3) ⋊ C5
HallC13⋊(D31⋊C5) ⋊ C32
HallC13⋊C3×C31⋊C3 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C32
HallD403 ⋊ C32×C5
HallΓL(1,𝔽32) ⋊ C3×D13⋊C3
SylowC31 ⋊ C3×C5×D13⋊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

Polycyclic presentation:

2,3^2,5,13,31|e^a=e^12,f^a=f^30,f^b=f^5,e^c=e^3,f^d=f^16

Conjugacy classes & character table

127 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 74);