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C11⋊PSU(3,𝔽2) #11716285

order792
isoclinismisoclinic class of C11⋊PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC11⋊PSU(3,𝔽2)

Splittings

Fitting, socle, HallC32×C11 ⋊ Q8
SylowC11 ⋊ PSU(3,𝔽2)
SylowC32 ⋊ Dic22

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, prime radical, cosocleC11×C3⋊D3C22
Fitting, socle, hypocenterC32×C11Q8
LCSG ▷ C11×C3⋊D3 ▷ C32×C11
UCSC1

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 99

Polycyclic presentation:

2^3,3^2,11|a^2=c,b^2=c,b^a=bc,d^a=e,e^a=d^2,f^a=f^10,d^b=de^2,e^b=d^2e^2,d^c=d^2,e^c=e^2

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13097490, AGL(1,𝔽9)⋊D11, D11×PSU(3,𝔽2), …
maximal normal subgroup of#13097490, AGL(1,𝔽9)⋊D11, D11×PSU(3,𝔽2), …
maximal quotient of#13097238, #13097239, C2×C11⋊PSU(3,𝔽2)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(792, 115);