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C2×C3⋊(Dic11⋊C5) #13050332

order1320
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(Dic11⋊C5)
unambiguous semidirect product(C2×C3)⋊(Dic11⋊C5)
unambiguous semidirect product(C2×C11⋊C5)⋊Dic3
unambiguous semidirect product(C2×Dic33)⋊C5

Splittings

derived, HallC3×C11 ⋊ C2×C4×C5
HallC2×Dic33 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×C4
HallC11⋊C5 ⋊ C2×Dic3
SylowC11 ⋊ C2×C5×Dic3
SylowC3 ⋊ C2×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC22C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C2×C4×C5
FrattiniC2C2×C3⋊AGL(1,𝔽11)
Fitting, socleC22×C3×C11C2×C5
prime radicalC22×C3×C11⋊C5C2
cosocleC2×C3×C11C22×C5
LCSG ▷ C3×C11
UCSC1 ◁ C22

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 264

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C4×C3⋊AGL(1,𝔽11), C2×D3×Dic11⋊C5, C2×Dic3×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C4×C3⋊AGL(1,𝔽11), C2×D3×Dic11⋊C5, C2×Dic3×AGL(1,𝔽11), …
maximal quotient of#72216822, #72217167

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 36);