Finite Group Databasebeta

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C3×A4×C71⋊C7 #31822062

order17892
automorphism?
homologyAbelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C71⋊C7
unambiguous semidirect productC22⋊(C32×C71⋊C7)
unambiguous semidirect product(C22×C3)⋊(C3×C71⋊C7)
unambiguous semidirect productC71⋊(C3×C7×A4)
unambiguous semidirect product(C3×C71)⋊(C7×A4)
unambiguous semidirect product(A4×C71)⋊(C3×C7)
unambiguous semidirect product(C22×C71⋊C7)⋊C32
unambiguous semidirect product(C3×A4×C71)⋊C7
unambiguous semidirect product(C22×C3×C71⋊C7)⋊C3

Splittings

Fitting, socleC22×C3×C71 ⋊ C3×C7
derived, HallC22×C71 ⋊ C32×C7
HallC3×A4×C71 ⋊ C7
HallC22×C71⋊C7 ⋊ C32
SylowC71 ⋊ C3×C7×A4
SylowC22 ⋊ C32×C71⋊C7

Subgroups

subgroupG/H
center, hypercenterC3A4×C71⋊C7
commutator, cosocle, hypocenterC22×C71C32×C7
FrattiniC1G
Fitting, socleC22×C3×C71C3×C7
LCSG ▷ C22×C71
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 852

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 79);