Finite Group Databasebeta

← Prev (#22575080) Next (#22575082) →

C11⋊C5×C3⋊#261 #22575081

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

Aliases

direct productC11⋊C5×C3⋊#261
unambiguous semidirect productC3⋊(#261×C11⋊C5)
unambiguous semidirect product(C11×C3⋊#261)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C13 ⋊ C4×C5
HallC3×C13×C11⋊C5 ⋊ C4
HallC11×C3⋊#261 ⋊ C5
HallC13×C11⋊C5 ⋊ Dic3
HallC3×C11⋊C5 ⋊ #261
HallC11×C13 ⋊ C5×Dic3
HallC3×C13 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×#261
SylowC13 ⋊ Dic3×C11⋊C5
SylowC11 ⋊ C5×C3⋊#261
SylowC3 ⋊ #261×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C13C4×C5
LCSG ▷ C3×C11×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×C9⋊#261, C11⋊C5×C3⋊AGL(1,𝔽13), C3×C11⋊C5×C3⋊#261, …
maximal normal subgroup ofC11⋊C5×C3⋊AGL(1,𝔽13), C3×C11⋊C5×C3⋊#261
maximal quotient ofC11⋊C5×C9⋊#261, C3×C11⋊C5×C3⋊#261, C11⋊C5×C3⋊(C3⋊#261)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 53);