Finite Group Databasebeta

← Prev (#22575138) Next (#22575140) →

C5×C11×C3⋊#261 #22575139

order8580
isoclinismisoclinic class of C3⋊#261
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C4
derived, HallC3×C13 ⋊ C4×C5×C11
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ C4×C11
HallC3×C5×C11 ⋊ #261
HallC11×C13 ⋊ C5×Dic3
HallC5×C13 ⋊ C11×Dic3
HallC3×C11 ⋊ C5×#261
HallC3×C5 ⋊ C11×#261
SylowC13 ⋊ C5×C11×Dic3
SylowC3 ⋊ C5×C11×#261

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊#261
commutator, hypocenterC3×C13C4×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C4
LCSG ▷ C3×C13
UCSC1 ◁ C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

825 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C11×C9⋊#261, C5×C11×C3⋊AGL(1,𝔽13), C3×C5×C11×C3⋊#261, …
maximal normal subgroup ofC5×C11×C3⋊AGL(1,𝔽13), C3×C5×C11×C3⋊#261
maximal quotient ofC5×C11×C9⋊#261, C3×C5×C11×C3⋊#261, C5×C11×C3⋊(C3⋊#261)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 111);