D₃×A₄×ΓL(1,𝔽₈) #13094902

order	1512
isoclinism	isoclinic class of D₃×A₄×ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	D₃×A₄×ΓL(1,𝔽₈)
unambiguous semidirect product	C₃⋊(C₂×A₄×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂²×D₃×ΓL(1,𝔽₈))⋊C₃
unambiguous semidirect product	(D₃×C₇×A₄)⋊C₃
unambiguous semidirect product	(D₃×C₂²⋊ΓL(1,𝔽₈))⋊C₃

Fitting, socle, derived	C₂²×C₃×C₇ ⋊ C₂×C₃²
Sylow	C₇ ⋊ C₃×D₃×A₄

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₃×C₇	C₂×C₃²
LCS	G ▷ C₂²×C₃×C₇
UCS	C₁

162 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.

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

μ_t(G) = 84

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 799);