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C2×C7×(C13⋊C3)⋊D19 #35209043

order20748
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×(C13⋊C3)⋊D19
unambiguous semidirect product(C2×C13⋊C3)⋊(C7×D19)

Splittings

Fitting, socleC2×C7×C13×C19 ⋊ C2×C3
derived, HallC13×C19 ⋊ C22×C3×C7
HallC2×C7×D247 ⋊ C3
HallC7×C19×C13⋊C3 ⋊ C22
HallC7×C13×C19 ⋊ C22×C3
HallC2×D247 ⋊ C3×C7
HallC19×C13⋊C3 ⋊ C22×C7
HallC7×C13⋊C3 ⋊ C2×D19
HallC7×C19 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D19
HallC13⋊C3 ⋊ C2×C7×D19
SylowC19 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D19

Subgroups

subgroupG/H
center, hypercenterC2×C7(C13⋊C3)⋊D19
commutator, cosocle, hypocenterC13×C19C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C13×C19C2×C3
LCSG ▷ C13×C19
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3458

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 271);