Finite Group Databasebeta

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C3×C13×D43⋊C7 #37553446

order23478
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D43⋊C7
unambiguous semidirect product(C3×D43)⋊(C7×C13)
unambiguous semidirect product(C3×C13×D43)⋊C7

Splittings

Fitting, socle, HallC3×C13×C43 ⋊ C2×C7
derived, SylowC43 ⋊ C2×C3×C7×C13
HallC3×C13×C43⋊C7 ⋊ C2
HallC13×C43⋊C7 ⋊ C2×C3
HallC3×C13×D43 ⋊ C7
HallC13×D43 ⋊ C3×C7
HallC3×C43⋊C7 ⋊ C2×C13
HallC13×C43 ⋊ C2×C3×C7
HallC43⋊C7 ⋊ C2×C3×C13
HallC3×D43 ⋊ C7×C13
HallC3×C43 ⋊ C2×C7×C13
HallD43 ⋊ C3×C7×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13D43⋊C7
commutator, cosocle, hypocenterC43C2×C3×C7×C13
FrattiniC1G
Fitting, socleC3×C13×C43C2×C7
LCSG ▷ C43
UCSC1 ◁ C3×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1677

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 35);