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C3×(C11⋊C5)⋊C8 #13050297

order1320
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C11⋊C5)⋊C8
unambiguous semidirect product(C11⋊C5)⋊(C3×C8)
unambiguous semidirect product(C11⋊C8)⋊(C3×C5)
unambiguous semidirect product(C3×C11⋊C8)⋊C5

Splittings

derived, SylowC11 ⋊ C3×C5×C8
HallC3×C11⋊C8 ⋊ C5
HallC3×C11⋊C5 ⋊ C8
HallC11⋊C8 ⋊ C3×C5
HallC11⋊C5 ⋊ C3×C8
HallC3×C11 ⋊ C5×C8

Subgroups

subgroupG/H
center, hypercenterC3×C4AGL(1,𝔽11)
commutator, hypocenterC11C3×C5×C8
FrattiniC4C3×AGL(1,𝔽11)
FittingC3×C4×C11C2×C5
socleC2×C3×C11C4×C5
prime radicalC2×C3×C11⋊C5C4
cosocleC4×C11C2×C3×C5
LCSG ▷ C11
UCSC1 ◁ C3×C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3)(4,5,6,8,7,9,10,11)(13,16,17,21,20,14,15,18,19,22);(12,13,16,19,17,20,22,18,21,15,14)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C8×AGL(1,𝔽11), C3×#4313⋊C5, D3×(C11⋊C5)⋊C8, …
maximal normal subgroup ofC3×C8×AGL(1,𝔽11), C3×#4313⋊C5, D3×(C11⋊C5)⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 1);