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D13×(C43⋊C3)⋊C7 #37553548

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

Aliases

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

Splittings

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

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 137);