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C2×C3×Dic11⋊C5 #13050322

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

Aliases

direct productC2×C3×Dic11⋊C5
unambiguous semidirect product(C2×Dic11)⋊(C3×C5)
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×C4)
unambiguous semidirect product(C2×C3×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C2×C3×C4×C5
HallC2×C3×Dic11 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×C4
HallC2×Dic11 ⋊ C3×C5
HallC11⋊C5 ⋊ C2×C3×C4
HallC3×C11 ⋊ C2×C4×C5

Subgroups

subgroupG/H
center, hypercenterC22×C3AGL(1,𝔽11)
commutator, hypocenterC11C2×C3×C4×C5
FrattiniC2C2×C3×AGL(1,𝔽11)
Fitting, socleC22×C3×C11C2×C5
prime radicalC22×C3×C11⋊C5C2
cosocleC2×C11C22×C3×C5
LCSG ▷ C11
UCSC1 ◁ C22×C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 264

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×C4×AGL(1,𝔽11), C2×D3×Dic11⋊C5, C2×(D33⋊C4)⋊C5, …
maximal normal subgroup ofC2×C3×C4×AGL(1,𝔽11), C2×D3×Dic11⋊C5, C2×(D33⋊C4)⋊C5, …
maximal quotient ofC3×#4318⋊C5, C3×C22⋊(Dic11⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 26);