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C2×C3×C4×C11⋊C5 #13050334

order1320
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4C11⋊C5
commutator, hypocenterC11C2×C3×C4×C5
FrattiniC2C22×C3×C11⋊C5
FittingC2×C3×C4×C11C5
socleC22×C3×C11C2×C5
prime radicalC22×C3×C11⋊C5C2
cosocleC2×C11C22×C3×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C4

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 264

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2)(7,8,9)(11,12,14,17,16)(13,15,19,20,18);(3,4,5,6)(10,11,13,16,12,14,18,20,15,17,19)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×C4×AGL(1,𝔽11), C2×C4×D3×C11⋊C5, C2×C4×C3⋊AGL(1,𝔽11), …
maximal normal subgroup ofC2×C3×C4×AGL(1,𝔽11), C2×C4×D3×C11⋊C5, C2×C4×C3⋊AGL(1,𝔽11), …
maximal quotient ofC3×M16×C11⋊C5, C3×C22⋊C4×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 38);