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C7×(C13⋊C3)⋊D43 #37553480

order23478
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C13⋊C3)⋊D43
unambiguous semidirect product(C13⋊C3)⋊(C7×D43)

Splittings

Fitting, socle, HallC7×C13×C43 ⋊ C2×C3
derived, HallC13×C43 ⋊ C2×C3×C7
HallC7×C13⋊C3×C43 ⋊ C2
HallC7×D559 ⋊ C3
HallC13⋊C3×C43 ⋊ C2×C7
HallD559 ⋊ C3×C7
HallC7×C43 ⋊ D13⋊C3
HallC7×C13⋊C3 ⋊ D43
HallC7×C13 ⋊ C3×D43
SylowC43 ⋊ C7×D13⋊C3
HallC13⋊C3 ⋊ C7×D43
SylowC13 ⋊ C3×C7×D43

Subgroups

subgroupG/H
center, hypercenterC7(C13⋊C3)⋊D43
commutator, cosocle, hypocenterC13×C43C2×C3×C7
FrattiniC1G
Fitting, socleC7×C13×C43C2×C3
LCSG ▷ C13×C43
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3913

Conjugacy classes & character table

1085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 69);