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C3×D7×D71⋊C5 #44447184

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×D7×D71⋊C5
unambiguous semidirect productD71⋊(C3×C5×D7)
unambiguous semidirect product(C3×D7×D71)⋊C5

Splittings

Fitting, socle, HallC3×C7×C71 ⋊ C22×C5
derived, HallC7×C71 ⋊ C22×C3×C5
HallC3×C7×C71⋊C5 ⋊ C22
HallC3×D7×D71 ⋊ C5
HallC7×C71⋊C5 ⋊ C22×C3
HallD7×D71 ⋊ C3×C5
HallC3×C71⋊C5 ⋊ C2×D7
HallC71⋊C5 ⋊ C2×C3×D7
HallC3×C71 ⋊ C2×C5×D7
SylowC71 ⋊ C2×C3×C5×D7
HallC3×C7 ⋊ C2×D71⋊C5
SylowC7 ⋊ C2×C3×D71⋊C5

Subgroups

subgroupG/H
center, hypercenterC3D7×D71⋊C5
commutator, cosocle, hypocenterC7×C71C22×C3×C5
FrattiniC1G
Fitting, socleC3×C7×C71C22×C5
LCSG ▷ C7×C71
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1491

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 72);