Finite Group Databasebeta

← Prev (#44544661) Next (#44544663) →

C22×C9×C127⋊C7 #44544662

order32004
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C9×C127⋊C7
unambiguous semidirect product(C22×C9×C127)⋊C7

Splittings

Fitting, HallC22×C9×C127 ⋊ C7
derived, SylowC127 ⋊ C22×C7×C9
HallC9×C127 ⋊ C22×C7
HallC22×C127 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC22×C9C127⋊C7
commutator, hypocenterC127C22×C7×C9
FrattiniC3C22×C3×C127⋊C7
FittingC22×C9×C127C7
socleC22×C3×C127C3×C7
prime radicalC22×C3×C127⋊C7C3
cosocleC3×C127C22×C3×C7
LCSG ▷ C127
UCSC1 ◁ C22×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4572

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 44);