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C19⋊C3×D31⋊C5 #31799005

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

Aliases

direct productC19⋊C3×D31⋊C5
unambiguous semidirect product(C19⋊C3×D31)⋊C5

Splittings

Fitting, socle, derived, HallC19×C31 ⋊ C2×C3×C5
HallC19⋊C3×ΓL(1,𝔽32) ⋊ C2
HallC19×D31⋊C5 ⋊ C3
HallC19⋊C3×D31 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×C3
HallC31×C19⋊C3 ⋊ C2×C5
HallC19×D31 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ C2×C19⋊C3
HallD31 ⋊ C5×C19⋊C3
SylowC31 ⋊ C2×C5×C19⋊C3
SylowC19 ⋊ C3×D31⋊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

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×D31⋊C5, C2×C19⋊C3×D31⋊C5
maximal normal subgroup ofD19⋊C3×D31⋊C5, C2×C19⋊C3×D31⋊C5
maximal quotient ofC19⋊C3×Dic31⋊C5, C2×C19⋊C3×D31⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 62);