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(C5⋊(D19⋊C3))⋊D31 #47977669

order35340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C5⋊(D19⋊C3))⋊D31
unambiguous semidirect product((C19⋊C3)⋊D31)⋊D5

Splittings

Fitting, socle, derived, HallC5×C19×C31 ⋊ C22×C3
HallD95⋊D31 ⋊ C3
HallC5×C31×C19⋊C3 ⋊ C22
HallC31×C19⋊C3 ⋊ C2×D5
HallC19×C31 ⋊ C2×C3×D5
HallC5×C19⋊C3 ⋊ C2×D31
HallC5×C31 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C2×C3×D31
HallC19⋊C3 ⋊ D5×D31
SylowC31 ⋊ D5×D19⋊C3
SylowC19 ⋊ C3×D5×D31
SylowC5 ⋊ D31×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C31C22×C3
LCSG ▷ C5×C19×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Polycyclic presentation:

2^2,3,5,19,31|e^a=e^18,f^a=f^30,d^b=d^4,e^b=e^18,e^c=e^7

Conjugacy classes & character table

441 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 141);