Finite Group Databasebeta

← Prev (#13050324) Next (#13050326) →

C4×D3×C11⋊C5 #13050325

order1320
isoclinismisoclinic class of D3×C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC4×D3×C11⋊C5
unambiguous semidirect product(C4×D3×C11)⋊C5

Splittings

FittingC3×C4×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C4×C5
HallC4×D3×C11 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×C4
SylowC11 ⋊ C4×C5×D3
SylowC3 ⋊ C2×C4×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC4D3×C11⋊C5
commutator, hypocenterC3×C11C2×C4×C5
FrattiniC2C2×D3×C11⋊C5
FittingC3×C4×C11C2×C5
socle, cosocleC2×C3×C11C22×C5
prime radicalC2×D3×C11⋊C5C2
LCSG ▷ C3×C11
UCSC1 ◁ C4

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D3×AGL(1,𝔽11), C2×C4×D3×C11⋊C5, D3×D4×C11⋊C5, …
maximal normal subgroup ofC4×D3×AGL(1,𝔽11), C2×C4×D3×C11⋊C5, D3×D4×C11⋊C5, …
maximal quotient ofC2×C4×D3×C11⋊C5, D3×C8×C11⋊C5, ΓL(1,𝔽25)×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 29);