Finite Group Databasebeta

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C7×(C13⋊C3)⋊(D19⋊C3) #44527644

order31122
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×(C13⋊C3)⋊(D19⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C7×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C7×D13⋊C3)
unambiguous semidirect product((C19⋊C3)⋊D13)⋊(C3×C7)
unambiguous semidirect product((C13⋊C3)⋊D19)⋊(C3×C7)
unambiguous semidirect product#13093366⋊(C3×C7)
unambiguous semidirect product#13093367⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C32
derived, HallC13×C19 ⋊ C2×C32×C7
HallC7×C13⋊C3×C19⋊C3 ⋊ C2
HallC7×D247 ⋊ C32
HallC13⋊C3×C19⋊C3 ⋊ C2×C7
HallD247 ⋊ C32×C7
HallC7×C19 ⋊ C3×D13⋊C3
HallC7×C13 ⋊ C3×D19⋊C3
SylowC19 ⋊ C3×C7×D13⋊C3
SylowC13 ⋊ C3×C7×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC7(C13⋊C3)⋊(D19⋊C3)
commutator, cosocle, hypocenterC13×C19C2×C32×C7
FrattiniC1G
Fitting, socleC7×C13×C19C2×C32
LCSG ▷ C13×C19
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1729

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 127);