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C3×(C13⋊C3)⋊D133 #44527897

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

Aliases

direct productC3×(C13⋊C3)⋊D133
unambiguous semidirect product(C13⋊C3)⋊(C3×D133)

Splittings

Fitting, socleC3×C7×C13×C19 ⋊ C2×C3
derived, HallC7×C13×C19 ⋊ C2×C32
HallC3×C7×C19×C13⋊C3 ⋊ C2
HallD1729 ⋊ C32
HallC3×C19×C13⋊C3 ⋊ D7
HallC3×C7×C13⋊C3 ⋊ D19
HallC13×C19 ⋊ C32×D7
HallC7×C19 ⋊ C3×D13⋊C3
HallC3×C13⋊C3 ⋊ D133
HallC7×C13 ⋊ C32×D19
SylowC19 ⋊ C3×(C13⋊C3)⋊D7
SylowC13 ⋊ C32×D133
SylowC7 ⋊ C3×(C13⋊C3)⋊D19

Subgroups

subgroupG/H
center, hypercenterC3(C13⋊C3)⋊D133
commutator, cosocle, hypocenterC7×C13×C19C2×C32
FrattiniC1G
Fitting, socleC3×C7×C13×C19C2×C3
LCSG ▷ C7×C13×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5187

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 380);