ΓL(1,𝔽₈)×C₃⋊(C₁₉⋊AGL(1,𝔽₅)) #37561331

order	23940
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	ΓL(1,𝔽₈)×C₃⋊(C₁₉⋊AGL(1,𝔽₅))
unambiguous semidirect product	C₃⋊(ΓL(1,𝔽₈)×C₁₉⋊AGL(1,𝔽₅))

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₇×C₁₉	C₃×C₄
prime radical	C₃×D₅×C₁₉×ΓL(1,𝔽₈)	C₂
cosocle	C₃×C₇×D₅×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₅×C₇×C₁₉
UCS	C₁

112 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

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

μ_t(G) = 1995

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 463);