Finite Group Databasebeta

← Prev (#22575071) Next (#22575073) →

C3×(C11⋊C5)⋊#261 #22575072

order8580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C11×C13 ⋊ C4×C5
derived, HallC11×C13 ⋊ C3×C4×C5
HallC3×C13×C11⋊C5 ⋊ C4
HallC3×C11⋊#261 ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C4
HallC11⋊#261 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ #261
HallC11⋊C5 ⋊ C3×#261
HallC3×C13 ⋊ Dic11⋊C5
HallC3×C11 ⋊ C5×#261
SylowC13 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C3×C5×#261

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊#261
commutator, hypocenterC11×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C11×C13C4×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C11⋊C5)⋊(#261⋊C9), C9×(C11⋊C5)⋊#261, C3×(C11⋊C5)⋊AGL(1,𝔽13), …
maximal normal subgroup of(C11⋊C5)⋊(#261⋊C9), C9×(C11⋊C5)⋊#261, C3×(C11⋊C5)⋊AGL(1,𝔽13), …
maximal quotient ofC9×(C11⋊C5)⋊#261, C32×(C11⋊C5)⋊#261, C3×C3⋊((C11⋊C5)⋊#261)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 44);