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(C31⋊C3)⋊(C19⋊AGL(1,𝔽5)) #47977652

order35340
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C31⋊C3)⋊(C19⋊AGL(1,𝔽5))

Splittings

Fitting, socle, derived, HallC5×C19×C31 ⋊ C3×C4
HallC19⋊(C31⋊AGL(1,𝔽5)) ⋊ C3
HallC5×C19×C31⋊C3 ⋊ C4
HallC19×C31⋊C3 ⋊ AGL(1,𝔽5)
HallC19×C31 ⋊ C3×AGL(1,𝔽5)
HallC5×C31⋊C3 ⋊ Dic19
HallC5×C31 ⋊ C3×Dic19
HallC5×C19 ⋊ (C31⋊C3)⋊C4
HallC31⋊C3 ⋊ C19⋊AGL(1,𝔽5)
SylowC31 ⋊ C3×C19⋊AGL(1,𝔽5)
SylowC19 ⋊ (C31⋊C3)⋊AGL(1,𝔽5)
SylowC5 ⋊ (C31⋊C3)⋊Dic19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C19×C31C3×C4
prime radicalD5×C19×C31⋊C3C2
cosocleD5×C19×C31C2×C3
LCSG ▷ C5×C19×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Polycyclic presentation:

2,3,2,5,19,31|a^2=c,d^a=d^2,e^a=e^18,f^a=f^30,f^b=f^5,d^c=d^4

Conjugacy classes & character table

503 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 124);