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C3×C11×SL(2,𝔽3) #11716249

order792
isoclinismisoclinic class of SL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×SL(2,𝔽3)
unambiguous semidirect productQ8⋊(C32×C11)
unambiguous semidirect product(C3×Q8)⋊(C3×C11)
unambiguous semidirect product(Q8×C11)⋊C32
unambiguous semidirect product(C3×Q8×C11)⋊C3

Splittings

FittingC3×Q8×C11 ⋊ C3
derived, SylowQ8 ⋊ C32×C11
HallQ8×C11 ⋊ C32

Subgroups

subgroupG/H
center, socle, hypercenterC2×C3×C11A4
commutator, cosocle, hypocenterQ8C32×C11
FrattiniC2C3×C11×A4
FittingC3×Q8×C11C3
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 264

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC3⋊(C11⋊#226), C3⋊(C11⋊GL(2,𝔽3))
maximal subgroup ofC3×C11×#226, C3×C11×GL(2,𝔽3), C3×C11⋊#226, …
maximal normal subgroup ofC3×C11×#226, C3×C11×GL(2,𝔽3), C3×C11⋊#226, …
maximal quotient ofC2×C3×C11×SL(2,𝔽3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(792, 79);