Finite Group Databasebeta

← Prev (#38787925) Next (#38787927) →

C2×C11×C13×D45 #38787926

order25740
automorphism?
homologyAbelianization (H1) = C22×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C13×D45
unambiguous semidirect product(C2×C5)⋊(C11×C13×D9)
unambiguous semidirect product(C2×C9)⋊(D5×C11×C13)

Splittings

FittingC2×C5×C9×C11×C13 ⋊ C2
derived, HallC5×C9 ⋊ C22×C11×C13
HallC5×C9×C11×C13 ⋊ C22
HallC9×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×D9
HallC5×C9×C13 ⋊ C22×C11
HallC5×C9×C11 ⋊ C22×C13
HallC9×C13 ⋊ C2×D5×C11
HallC9×C11 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×C11×D9
HallC5×C11 ⋊ C2×C13×D9
SylowC9 ⋊ C2×D5×C11×C13
SylowC5 ⋊ C2×C11×C13×D9

Subgroups

subgroupG/H
center, hypercenterC2×C11×C13D45
commutator, cosocle, hypocenterC5×C9C22×C11×C13
FrattiniC3C2×C11×C13×D15
FittingC2×C5×C9×C11×C13C2
socleC2×C3×C5×C11×C13D3
LCSG ▷ C5×C9
UCSC1 ◁ C2×C11×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12870

Conjugacy classes & character table

6864 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 157);