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((C31⋊C3)⋊C5)⋊Dic17 #44539279

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

Aliases

unambiguous semidirect product((C31⋊C3)⋊C5)⋊Dic17
unambiguous semidirect product((C31⋊C3)⋊Dic17)⋊C5
unambiguous semidirect product(ΓL(1,𝔽32)⋊Dic17)⋊C3

Splittings

derived, HallC17×C31 ⋊ C3×C4×C5
HallΓL(1,𝔽32)⋊Dic17 ⋊ C3
HallC17×(C31⋊C3)⋊C5 ⋊ C4
Hall(C31⋊C3)⋊Dic17 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C3×C4
HallDic527 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
Hall(C31⋊C3)⋊C5 ⋊ Dic17
HallΓL(1,𝔽32) ⋊ C3×Dic17
HallC31⋊C3 ⋊ C5×Dic17
SylowC31 ⋊ C3×C5×Dic17
SylowC17 ⋊ ((C31⋊C3)⋊C4)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C17⋊AGL(1,𝔽31)
commutator, hypocenterC17×C31C3×C4×C5
Fitting, socle, cosocleC2×C17×C31C2×C3×C5
prime radicalC2×C17×(C31⋊C3)⋊C5C2
LCSG ▷ C17×C31
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2108

Polycyclic presentation:

2,3,5,17,31,2|a^2=f,d^a=d^16,e^a=e^30,e^b=e^25,e^c=e^16

Conjugacy classes & character table

334 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 36);