Finite Group Databasebeta

← Prev (#38787808) Next (#38787810) →

C11⋊C5×#261⋊C9 #38787809

order25740
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×#261⋊C9
unambiguous semidirect product#261⋊(C9×C11⋊C5)
unambiguous semidirect product(#261×C11⋊C5)⋊C9
unambiguous semidirect product(C11×#261⋊C9)⋊C5

Splittings

derived, HallC11×C13 ⋊ C4×C5×C9
HallC11⋊C5×C13⋊C9 ⋊ C4
HallC11×#261⋊C9 ⋊ C5
Hall#261×C11⋊C5 ⋊ C9
HallC11×C13⋊C9 ⋊ C4×C5
HallC13×C11⋊C5 ⋊ C4×C9
HallC11×#261 ⋊ C5×C9
HallC13⋊C9 ⋊ C4×C11⋊C5
Hall#261 ⋊ C9×C11⋊C5
SylowC13 ⋊ C4×C9×C11⋊C5
SylowC11 ⋊ C5×#261⋊C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC3C11⋊C5×AGL(1,𝔽13)
commutator, hypocenterC11×C13C4×C5×C9
Fitting, socleC3×C11×C13C3×C4×C5
prime radicalC3×D13×C11⋊C5C2×C3
cosocleC3×C11×D13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1287

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 40);