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C3×C7×D71⋊C7 #35229443

order20874
automorphism?
homologyAbelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C7×D71⋊C7
unambiguous semidirect productD71⋊(C3×C72)
unambiguous semidirect product(C3×D71)⋊C72
unambiguous semidirect product(C71⋊C7)⋊(C2×C3×C7)
unambiguous semidirect product(C3×C7×D71)⋊C7

Splittings

Fitting, socleC3×C7×C71 ⋊ C2×C7
derived, SylowC71 ⋊ C2×C3×C72
HallC3×C7×C71⋊C7 ⋊ C2
HallC7×C71⋊C7 ⋊ C2×C3
HallC3×D71 ⋊ C72
HallC3×C71 ⋊ C2×C72
HallD71 ⋊ C3×C72

Subgroups

subgroupG/H
center, hypercenterC3×C7D71⋊C7
commutator, cosocle, hypocenterC71C2×C3×C72
FrattiniC1G
Fitting, socleC3×C7×C71C2×C7
LCSG ▷ C71
UCSC1 ◁ C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1491

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20874, 22);