S₄×AGL(1,𝔽₇) #11759715

order	1008
isoclinism	isoclinic class of S₄×AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	S₄×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃×S₄)
unambiguous semidirect product	(D₇×S₄)⋊C₃
unambiguous semidirect product	(ΓL(1,𝔽₈)×S₄)⋊C₂
unambiguous semidirect product	(A₄⋊AGL(1,𝔽₇))⋊C₂
unambiguous semidirect product	(A₄×AGL(1,𝔽₇))⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₇×A₄	C₂²×C₃
Fitting, socle	C₂²×C₇	C₂×C₃×D₃
LCS	G ▷ C₇×A₄
UCS	C₁

140 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.

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

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 28

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 886);