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C19×((C31⋊C3)⋊C4)⋊C5 #47977589

order35340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×((C31⋊C3)⋊C4)⋊C5
unambiguous semidirect product((C31⋊C3)⋊C4)⋊(C5×C19)
unambiguous semidirect product((C31⋊C3)⋊C5)⋊(C4×C19)
unambiguous semidirect product(Dic31⋊C5)⋊(C3×C19)
unambiguous semidirect product(C19×(C31⋊C3)⋊C4)⋊C5

Splittings

derived, SylowC31 ⋊ C3×C4×C5×C19
HallC19×Dic31⋊C5 ⋊ C3
HallC19×(C31⋊C3)⋊C5 ⋊ C4
HallC19×(C31⋊C3)⋊C4 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C3×C4
HallC19×Dic31 ⋊ C3×C5
HallC19×C31⋊C3 ⋊ C4×C5
HallDic31⋊C5 ⋊ C3×C19
HallC19×C31 ⋊ C3×C4×C5
Hall(C31⋊C3)⋊C5 ⋊ C4×C19
Hall(C31⋊C3)⋊C4 ⋊ C5×C19
HallΓL(1,𝔽32) ⋊ C3×C4×C19
HallDic31 ⋊ C3×C5×C19
HallC31⋊C3 ⋊ C4×C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19AGL(1,𝔽31)
commutator, hypocenterC31C3×C4×C5×C19
FrattiniC2C19×AGL(1,𝔽31)
Fitting, socleC2×C19×C31C2×C3×C5
prime radicalC2×C19×(C31⋊C3)⋊C5C2
cosocleC2×C31C2×C3×C5×C19
LCSG ▷ C31
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2356

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 61);