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C2×C13⋊C3×C43⋊C7 #37553428

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

Aliases

direct productC2×C13⋊C3×C43⋊C7
unambiguous semidirect product(C2×C13)⋊(C3×C43⋊C7)
unambiguous semidirect product(C2×C13⋊C3×C43)⋊C7

Splittings

Fitting, socle, HallC2×C13×C43 ⋊ C3×C7
derived, HallC13×C43 ⋊ C2×C3×C7
HallC2×C13×C43⋊C7 ⋊ C3
HallC13×C43⋊C7 ⋊ C2×C3
HallC2×C13⋊C3×C43 ⋊ C7
HallC13⋊C3×C43 ⋊ C2×C7
HallC2×C43 ⋊ C7×C13⋊C3
SylowC43 ⋊ C2×C7×C13⋊C3
HallC2×C13 ⋊ C3×C43⋊C7
SylowC13 ⋊ C2×C3×C43⋊C7

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×C43⋊C7
commutator, cosocle, hypocenterC13×C43C2×C3×C7
FrattiniC1G
Fitting, socleC2×C13×C43C3×C7
LCSG ▷ C13×C43
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1118

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 17);