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Cayley diagram

D3×C11⋊C5 #66508

order330
isoclinismisoclinic class of D3×C11⋊C5
automorphismAut(G) = D3×AGL(1,𝔽11) (order 660) · Inn(G) = G · Out(G) = C2
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11⋊C5
unambiguous semidirect productC3⋊(C2×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11 ⋊ C2×C5
HallC3×C11⋊C5 ⋊ C2
HallD3×C11 ⋊ C5
SylowC11 ⋊ C5×D3
SylowC3 ⋊ C2×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11C2×C5
LCSG ▷ C3×C11
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 33

A minimal faithful permutation representation — 2 generators on 14 points:

(2,3)(5,6,8,11,10)(7,9,13,14,12);(1,2,3)(4,5,7,10,6,8,12,14,9,11,13)

Conjugacy classes & character table

21 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽11), C2×D3×C11⋊C5, D9×C11⋊C5, …
maximal normal subgroup ofD3×AGL(1,𝔽11), C2×D3×C11⋊C5, C3×D3×C11⋊C5, …
maximal quotient ofDic3×C11⋊C5, C2×D3×C11⋊C5, D9×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(330, 2);