C₃×A₄×AGL(1,𝔽₇) #13094901

order	1512
isoclinism	isoclinic class of A₄×AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₂×C₃³

Aliases

direct product	C₃×A₄×AGL(1,𝔽₇)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂×C₃×A₄)
unambiguous semidirect product	(C₂²×AGL(1,𝔽₇))⋊C₃²
unambiguous semidirect product	(A₄×D₇)⋊C₃²
unambiguous semidirect product	(D₇⋊A₄)⋊C₃²

	subgroup	G/H
center, hypercenter	C₃	A₄×AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₂²×C₇	C₂×C₃³
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇	C₂×C₃²
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₃

272 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 76 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, 798);