Finite Group Databasebeta

← Prev (#44539280) Next (#44539282) →

((C31⋊C3)⋊C5)⋊#595 #44539281

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product((C31⋊C3)⋊C5)⋊#595
unambiguous semidirect product((C31⋊C3)⋊#595)⋊C5
unambiguous semidirect product(ΓL(1,𝔽32)⋊#595)⋊C3

Splittings

Fitting, socle, derived, HallC17×C31 ⋊ C3×C4×C5
HallΓL(1,𝔽32)⋊#595 ⋊ C3
HallC17×(C31⋊C3)⋊C5 ⋊ C4
Hall(C31⋊C3)⋊#595 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C3×C4
HallC31⋊#595 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
Hall(C31⋊C3)⋊C5 ⋊ #595
HallΓL(1,𝔽32) ⋊ C3×#595
HallC31⋊C3 ⋊ C5×#595
SylowC31 ⋊ C3×C5×#595
SylowC17 ⋊ ((C31⋊C3)⋊C4)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC17×C31C3×C4×C5
prime radicalD17×(C31⋊C3)⋊C5C2
cosocleC31×D17C2×C3×C5
LCSG ▷ C17×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 527

Polycyclic presentation:

2,3,5,2,17,31|a^2=d,e^a=e^13,f^a=f^30,f^b=f^5,f^c=f^16,e^d=e^16

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 38);