Finite Group Databasebeta

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C3×C13⋊(D43⋊C7) #37553448

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

Aliases

direct productC3×C13⋊(D43⋊C7)
unambiguous semidirect product(C3×D559)⋊C7

Splittings

Fitting, socle, HallC3×C13×C43 ⋊ C2×C7
derived, HallC13×C43 ⋊ C2×C3×C7
HallC3×C13×C43⋊C7 ⋊ C2
HallC13×C43⋊C7 ⋊ C2×C3
HallC3×D559 ⋊ C7
HallD559 ⋊ C3×C7
HallC3×C43⋊C7 ⋊ D13
HallC43⋊C7 ⋊ C3×D13
HallC3×C43 ⋊ C7×D13
SylowC43 ⋊ C3×C7×D13
HallC3×C13 ⋊ D43⋊C7
SylowC13 ⋊ C3×D43⋊C7

Subgroups

subgroupG/H
center, hypercenterC3C13⋊(D43⋊C7)
commutator, cosocle, hypocenterC13×C43C2×C3×C7
FrattiniC1G
Fitting, socleC3×C13×C43C2×C7
LCSG ▷ C13×C43
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1677

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 37);