D₄×AΓL(1,𝔽₈) #13062018

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₄×AΓL(1,𝔽₈)
unambiguous semidirect product	C₄⋊(C₂×AΓL(1,𝔽₈))
unambiguous semidirect product	AGL(1,𝔽₈)⋊(C₃×D₄)
unambiguous semidirect product	(D₄×AGL(1,𝔽₈))⋊C₃
unambiguous semidirect product	(C₄×AΓL(1,𝔽₈))⋊C₂
unambiguous semidirect product	(C₂²×AΓL(1,𝔽₈))⋊C₂

Fitting, Sylow	C₂³×D₄ ⋊ ΓL(1,𝔽₈)
Hall	D₄×AGL(1,𝔽₈) ⋊ C₃

159 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 159 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 28

maximal subgroup of	D₄×AGL(3,𝔽₂), S₄×AΓL(1,𝔽₈)
automorphism group of	C₂×C₄×AGL(1,𝔽₈), D₄×AGL(1,𝔽₈)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 11307);