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C19×C3⋊((C13⋊C3)⋊D7) #44527996

order31122
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C3⋊((C13⋊C3)⋊D7)
unambiguous semidirect productC3⋊(C19×(C13⋊C3)⋊D7)
unambiguous semidirect product(C13⋊C3)⋊(C19×D21)

Splittings

Fitting, socleC3×C7×C13×C19 ⋊ C2×C3
derivedC3×C7×C13 ⋊ C2×C3×C19
HallC3×C7×C19×C13⋊C3 ⋊ C2
HallC3×C19×C13⋊C3 ⋊ D7
HallC7×C13×C19 ⋊ C3×D3
HallC3×C7×C13⋊C3 ⋊ C2×C19
HallC13×C19 ⋊ C3×D21
HallC7×C19 ⋊ C3⋊(D13⋊C3)
HallC3×C13⋊C3 ⋊ D7×C19
HallC7×C13 ⋊ C3×D3×C19
SylowC13 ⋊ C3×C19×D21
SylowC7 ⋊ C19×C3⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC19C3⋊((C13⋊C3)⋊D7)
commutator, cosocle, hypocenterC3×C7×C13C2×C3×C19
FrattiniC1G
Fitting, socleC3×C7×C13×C19C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5187

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 479);