Finite Group Databasebeta

← Prev (#38787870) Next (#38787872) →

C9×C11⋊#63120 #38787871

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

Aliases

direct productC9×C11⋊#63120
unambiguous semidirect productC11⋊(C9×#63120)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C4
derived, HallC5×C11×C13 ⋊ C4×C9
HallC9×C11×C13 ⋊ AGL(1,𝔽5)
HallC5×C9×C13 ⋊ Dic11
HallC5×C9×C11 ⋊ Dic13
HallC11×C13 ⋊ C9×AGL(1,𝔽5)
HallC9×C13 ⋊ C11⋊AGL(1,𝔽5)
HallC9×C11 ⋊ #63120
HallC5×C13 ⋊ C9×Dic11
HallC5×C11 ⋊ C9×Dic13
HallC5×C9 ⋊ Dic143
SylowC13 ⋊ C9×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ C9×#63120
SylowC5 ⋊ C9×Dic143

Subgroups

subgroupG/H
center, hypercenterC9C11⋊#63120
commutator, hypocenterC5×C11×C13C4×C9
FrattiniC3C3×C11⋊#63120
FittingC5×C9×C11×C13C4
socleC3×C5×C11×C13C3×C4
prime radical, cosocleC3×D5×C11×C13C2×C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

2601 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 102);