Finite Group Databasebeta

← Prev (#37553548) Next (#37553550) →

D13⋊C3×C43⋊C7 #37553549

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

Aliases

direct productD13⋊C3×C43⋊C7
unambiguous semidirect productD13⋊(C3×C43⋊C7)
unambiguous semidirect product(C13⋊C3)⋊(C2×C43⋊C7)
unambiguous semidirect product(C43×D13⋊C3)⋊C7

Splittings

Fitting, socle, derived, HallC13×C43 ⋊ C2×C3×C7
HallC13⋊C3×C43⋊C7 ⋊ C2
HallD13×C43⋊C7 ⋊ C3
HallC13×C43⋊C7 ⋊ C2×C3
HallC43×D13⋊C3 ⋊ C7
HallC13⋊C3×C43 ⋊ C2×C7
HallD13×C43 ⋊ C3×C7
SylowC43 ⋊ C7×D13⋊C3
HallC13⋊C3 ⋊ C2×C43⋊C7
HallD13 ⋊ C3×C43⋊C7
SylowC13 ⋊ C2×C3×C43⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C43C2×C3×C7
LCSG ▷ C13×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 559

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 138);