Finite Group Databasebeta

← Prev (#44539276) Next (#44539278) →

C17×((C31⋊C3)⋊C4)⋊C5 #44539277

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×((C31⋊C3)⋊C4)⋊C5
unambiguous semidirect product((C31⋊C3)⋊C4)⋊(C5×C17)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C4×C17)
unambiguous semidirect product(Dic31⋊C5)⋊(C3×C17)
unambiguous semidirect product(C17×(C31⋊C3)⋊C4)⋊C5
unambiguous semidirect product(C17×Dic31⋊C5)⋊C3

Splittings

derived, SylowC31 ⋊ C3×C4×C5×C17
HallC17×Dic31⋊C5 ⋊ C3
HallC17×(C31⋊C3)⋊C5 ⋊ C4
HallC17×(C31⋊C3)⋊C4 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C3×C4
HallC17×Dic31 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
HallDic31⋊C5 ⋊ C3×C17
HallC17×C31 ⋊ C3×C4×C5
Hall(C31⋊C3)⋊C5 ⋊ C4×C17
Hall(C31⋊C3)⋊C4 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ C3×C4×C17
HallDic31 ⋊ C3×C5×C17
HallC31⋊C3 ⋊ C4×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17AGL(1,𝔽31)
commutator, hypocenterC31C3×C4×C5×C17
FrattiniC2C17×AGL(1,𝔽31)
Fitting, socleC2×C17×C31C2×C3×C5
prime radicalC2×C17×(C31⋊C3)⋊C5C2
cosocleC2×C31C2×C3×C5×C17
LCSG ▷ C31
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2108

Conjugacy classes & character table

1054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 34);