Finite Group Databasebeta

← Prev (#41001247) Next (#41001249) →

C2×C9×D745 #41001248

order26820
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D745
unambiguous semidirect product(C2×C5)⋊(C9×D149)
unambiguous semidirect product(C2×C149)⋊(C9×D5)

Splittings

FittingC2×C5×C9×C149 ⋊ C2
derived, HallC5×C149 ⋊ C22×C9
HallC5×C9×C149 ⋊ C22
HallC9×C149 ⋊ C2×D5
SylowC149 ⋊ C2×C9×D5
HallC5×C9 ⋊ C2×D149
SylowC5 ⋊ C2×C9×D149

Subgroups

subgroupG/H
center, hypercenterC2×C9D745
commutator, hypocenterC5×C149C22×C9
FrattiniC3C2×C3×D745
FittingC2×C5×C9×C149C2
socleC2×C3×C5×C149C2×C3
prime radicalC2×C3×D745C3
cosocleC3×C5×C149C22×C3
LCSG ▷ C5×C149
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13410

Conjugacy classes & character table

6732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26820, 34);