Finite Group Databasebeta

← Prev (#44539368) Next (#44539370) →

C3⋊(C31⋊#66774) #44539369

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

Aliases

unambiguous semidirect productC3⋊(C31⋊#66774)
unambiguous semidirect productC31⋊(C3⋊#66774)

Splittings

Fitting, socle, derived, HallC3×C5×C17×C31 ⋊ C4
HallC5×C17×C31 ⋊ Dic3
HallC3×C17×C31 ⋊ AGL(1,𝔽5)
HallC17×C31 ⋊ ΓL(1,𝔽16)
HallC3×C5×C31 ⋊ Dic17
HallC3×C5×C17 ⋊ Dic31
HallC5×C31 ⋊ Dic51
HallC3×C31 ⋊ #66774
HallC5×C17 ⋊ Dic93
HallC3×C17 ⋊ C31⋊AGL(1,𝔽5)
SylowC31 ⋊ C3⋊#66774
SylowC17 ⋊ C3⋊(C31⋊AGL(1,𝔽5))
HallC3×C5 ⋊ Dic527
SylowC5 ⋊ Dic1581
SylowC3 ⋊ C31⋊#66774

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C17×C31C4
prime radical, cosocleC3×D5×C17×C31C2
LCSG ▷ C3×C5×C17×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Polycyclic presentation:

2^2,3,5,17,31|a^2=b,c^a=c^2,d^a=d^2,e^a=e^16,f^a=f^30,d^b=d^4

Conjugacy classes & character table

3165 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 126);