C₁₉×ΓL(1,𝔽₈)×AGL(1,𝔽₇) #30660669

order	16758
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₉×ΓL(1,𝔽₈)×AGL(1,𝔽₇)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂×C₁₉×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₇×AGL(1,𝔽₇))⋊(C₃×C₁₉)
unambiguous semidirect product	(D₇×ΓL(1,𝔽₈))⋊(C₃×C₁₉)
unambiguous semidirect product	#64422⋊(C₃×C₁₉)
unambiguous semidirect product	#64423⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	ΓL(1,𝔽₈)×AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇²	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₉	C₂×C₃²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₁₉

100 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.

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

μ_t(G) = 798

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 196);