Finite Group Databasebeta

← Prev (#37552501) Next (#37552503) →

C2×C9×D649 #37552502

order23364
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D649
unambiguous semidirect product(C2×C11)⋊(C9×D59)
unambiguous semidirect product(C2×C59)⋊(C9×D11)

Splittings

FittingC2×C9×C11×C59 ⋊ C2
derived, HallC11×C59 ⋊ C22×C9
HallC9×C11×C59 ⋊ C22
HallC9×C59 ⋊ C2×D11
HallC9×C11 ⋊ C2×D59
SylowC59 ⋊ C2×C9×D11
SylowC11 ⋊ C2×C9×D59

Subgroups

subgroupG/H
center, hypercenterC2×C9D649
commutator, hypocenterC11×C59C22×C9
FrattiniC3C2×C3×D649
FittingC2×C9×C11×C59C2
socleC2×C3×C11×C59C2×C3
prime radicalC2×C3×D649C3
cosocleC3×C11×C59C22×C3
LCSG ▷ C11×C59
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11682

Conjugacy classes & character table

5868 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23364, 22);