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C41×AGL(1,𝔽11) #17985240

order4510
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C5×C41)
unambiguous semidirect product(C11⋊C5)⋊(C2×C41)

Splittings

Fitting, socle, HallC11×C41 ⋊ C2×C5
derived, SylowC11 ⋊ C2×C5×C41
HallC41×C11⋊C5 ⋊ C2
HallD11×C41 ⋊ C5
HallC11⋊C5 ⋊ C2×C41
HallD11 ⋊ C5×C41

Subgroups

subgroupG/H
center, hypercenterC41AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C5×C41
FrattiniC1G
Fitting, socleC11×C41C2×C5
LCSG ▷ C11
UCSC1 ◁ C41

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 451

A minimal faithful permutation representation — 2 generators on 52 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(43,47,48,46,51,44,45,52,49,50);(42,43,46,51,45,48,52,47,50,49,44)

Conjugacy classes & character table

451 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C41×AGL(1,𝔽11), C41×C3⋊AGL(1,𝔽11), AGL(1,𝔽11)×C41⋊C5, …
maximal normal subgroup ofC3×C41×AGL(1,𝔽11), AGL(1,𝔽11)×C41⋊C5, C5×C41×AGL(1,𝔽11), …
maximal quotient ofC3×C41×AGL(1,𝔽11), C41×C3⋊AGL(1,𝔽11), C41×D11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4510, 22);