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ΓL(1,𝔽8)×C11⋊(D19⋊C3) #39911845

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

Aliases

direct productΓL(1,𝔽8)×C11⋊(D19⋊C3)
unambiguous semidirect productC11⋊(ΓL(1,𝔽8)×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(ΓL(1,𝔽8)×D11)
unambiguous semidirect product(C7×C11⋊(D19⋊C3))⋊C3
unambiguous semidirect product(ΓL(1,𝔽8)×D209)⋊C3
unambiguous semidirect product(C11⋊#11716321)⋊C3
unambiguous semidirect product(C11⋊#11716322)⋊C3

Splittings

Fitting, socle, derived, HallC7×C11×C19 ⋊ C2×C32
HallC11×ΓL(1,𝔽8)×C19⋊C3 ⋊ C2
HallC7×D209 ⋊ C32
HallΓL(1,𝔽8)×C19⋊C3 ⋊ D11
HallD209 ⋊ C3×ΓL(1,𝔽8)
HallC11×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×C19 ⋊ C32×D11
HallC7×C11 ⋊ C3×D19⋊C3
SylowC19 ⋊ C3×ΓL(1,𝔽8)×D11
SylowC11 ⋊ ΓL(1,𝔽8)×D19⋊C3
SylowC7 ⋊ C3×C11⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C19C2×C32
LCSG ▷ C7×C11×C19
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 72);