Finite Group Databasebeta

← Prev (#44447226) Next (#44447228) →

C22×C3×C7×C71⋊C5 #44447227

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C3×C7×C71⋊C5
unambiguous semidirect product(C22×C3×C7×C71)⋊C5

Splittings

Fitting, socle, HallC22×C3×C7×C71 ⋊ C5
derived, SylowC71 ⋊ C22×C3×C5×C7
HallC22×C7×C71 ⋊ C3×C5
HallC3×C7×C71 ⋊ C22×C5
HallC22×C3×C71 ⋊ C5×C7
HallC7×C71 ⋊ C22×C3×C5
HallC22×C71 ⋊ C3×C5×C7
HallC3×C71 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC22×C3×C7C71⋊C5
commutator, cosocle, hypocenterC71C22×C3×C5×C7
FrattiniC1G
Fitting, socleC22×C3×C7×C71C5
LCSG ▷ C71
UCSC1 ◁ C22×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5964

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 115);