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C2×C7×C13⋊C3×C19⋊C3 #44527796

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

Aliases

direct productC2×C7×C13⋊C3×C19⋊C3
unambiguous semidirect product(C2×C13×C19⋊C3)⋊(C3×C7)
unambiguous semidirect product(C2×C19×C13⋊C3)⋊(C3×C7)
unambiguous semidirect product(C2×#10625202)⋊(C3×C7)
unambiguous semidirect product(C2×#10625203)⋊(C3×C7)

Splittings

Fitting, socle, HallC2×C7×C13×C19 ⋊ C32
derived, HallC13×C19 ⋊ C2×C32×C7
HallC7×C13×C19 ⋊ C2×C32
HallC2×C13×C19 ⋊ C32×C7
HallC2×C7×C19 ⋊ C3×C13⋊C3
HallC2×C7×C13 ⋊ C3×C19⋊C3
HallC7×C19 ⋊ C2×C3×C13⋊C3
HallC7×C13 ⋊ C2×C3×C19⋊C3
HallC2×C19 ⋊ C3×C7×C13⋊C3
HallC2×C13 ⋊ C3×C7×C19⋊C3
SylowC19 ⋊ C2×C3×C7×C13⋊C3
SylowC13 ⋊ C2×C3×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7C13⋊C3×C19⋊C3
commutator, cosocle, hypocenterC13×C19C2×C32×C7
FrattiniC1G
Fitting, socleC2×C7×C13×C19C32
LCSG ▷ C13×C19
UCSC1 ◁ C2×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3458

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 279);