Finite Group Databasebeta

← Prev (#44447184) Next (#44447186) →

D3×C7×D71⋊C5 #44447185

order29820
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D71⋊C5
unambiguous semidirect product(D3×C7×D71)⋊C5

Splittings

Fitting, socle, HallC3×C7×C71 ⋊ C22×C5
derived, HallC3×C71 ⋊ C22×C5×C7
HallC3×C7×C71⋊C5 ⋊ C22
HallD3×C7×D71 ⋊ C5
HallC7×C71⋊C5 ⋊ C2×D3
HallC3×C71⋊C5 ⋊ C22×C7
HallD3×D71 ⋊ C5×C7
HallC7×C71 ⋊ C2×C5×D3
HallC71⋊C5 ⋊ C2×D3×C7
SylowC71 ⋊ C2×C5×D3×C7
HallC3×C7 ⋊ C2×D71⋊C5
SylowC3 ⋊ C2×C7×D71⋊C5

Subgroups

subgroupG/H
center, hypercenterC7D3×D71⋊C5
commutator, cosocle, hypocenterC3×C71C22×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C71C22×C5
LCSG ▷ C3×C71
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1491

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 73);