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C11×ΓL(1,𝔽8)×D19⋊C3 #39911840

order26334
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×ΓL(1,𝔽8)×D19⋊C3
unambiguous semidirect product(C19⋊C3)⋊(C2×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D19⋊C3)⋊(C3×C11)
unambiguous semidirect product(ΓL(1,𝔽8)×D19)⋊(C3×C11)
unambiguous semidirect product#11716321⋊(C3×C11)
unambiguous semidirect product#11716322⋊(C3×C11)
unambiguous semidirect product(C7×C11×D19⋊C3)⋊C3
unambiguous semidirect product(C11×ΓL(1,𝔽8)×D19)⋊C3
unambiguous semidirect product(C11×#11716321)⋊C3
unambiguous semidirect product(C11×#11716322)⋊C3

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C32
derived, HallC7×C19 ⋊ C2×C32×C11
HallC11×ΓL(1,𝔽8)×C19⋊C3 ⋊ C2
HallC7×C11×D19 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ C2×C11
HallC11×D19 ⋊ C3×ΓL(1,𝔽8)
HallC7×D19 ⋊ C32×C11
HallC11×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×D19⋊C3
HallD19 ⋊ C3×C11×ΓL(1,𝔽8)
SylowC19 ⋊ C2×C3×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×D19⋊C3
commutator, cosocle, hypocenterC7×C19C2×C32×C11
FrattiniC1G
Fitting, socleC7×C11×C19C2×C32
LCSG ▷ C7×C19
UCSC1 ◁ C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 67);