Finite Group Databasebeta

← Prev (#38788257) Next (#38788259) →

C5×C11×C3⋊(C3⋊#261) #38788258

order25740
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×C3⋊(C3⋊#261)
unambiguous semidirect productC3⋊(C5×C11×C3⋊#261)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC32×C13 ⋊ C4×C5×C11
HallC32×C11×C13 ⋊ C4×C5
HallC5×C11×C13 ⋊ C3⋊Dic3
HallC32×C5×C13 ⋊ C4×C11
HallC32×C5×C11 ⋊ #261
HallC11×C13 ⋊ C5×C3⋊Dic3
HallC32×C11 ⋊ C5×#261
HallC5×C13 ⋊ C11×C3⋊Dic3
HallC32×C5 ⋊ C11×#261
SylowC13 ⋊ C5×C11×C3⋊Dic3
SylowC32 ⋊ C5×C11×#261

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊(C3⋊#261)
commutator, hypocenterC32×C13C4×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C5×C11×D13C2
cosocleC32×D13C2×C5×C11
LCSG ▷ C32×C13
UCSC1 ◁ C5×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 489);