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D19×(C31⋊C3)⋊C5 #31799008

order17670
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD19×(C31⋊C3)⋊C5
unambiguous semidirect product(D19×C31⋊C3)⋊C5

Splittings

Fitting, socle, derived, HallC19×C31 ⋊ C2×C3×C5
HallC19×(C31⋊C3)⋊C5 ⋊ C2
HallD19×ΓL(1,𝔽32) ⋊ C3
HallD19×C31⋊C3 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×C3
HallC19×C31⋊C3 ⋊ C2×C5
HallC31×D19 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ C3×D19
HallC31⋊C3 ⋊ C5×D19
SylowC31 ⋊ C3×C5×D19
SylowC19 ⋊ C2×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C31C2×C3×C5
LCSG ▷ C19×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 589

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×AGL(1,𝔽31), C2×D19×(C31⋊C3)⋊C5
maximal normal subgroup ofD19×AGL(1,𝔽31), C2×D19×(C31⋊C3)⋊C5
maximal quotient ofDic19×(C31⋊C3)⋊C5, C2×D19×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 65);