C₃×C₅×(C₁₉⋊C₃)⋊AGL(1,𝔽₅) #30685734

order	17100
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₅ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₅×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)
unambiguous semidirect product	(C₁₉⋊C₃)⋊(C₃×C₅×AGL(1,𝔽₅))
unambiguous semidirect product	(C₁₉⋊AGL(1,𝔽₅))⋊(C₃²×C₅)
unambiguous semidirect product	(C₃×C₁₉⋊AGL(1,𝔽₅))⋊(C₃×C₅)
unambiguous semidirect product	(C₅×C₁₉⋊AGL(1,𝔽₅))⋊C₃²
unambiguous semidirect product	(C₃×C₅×C₁₉⋊AGL(1,𝔽₅))⋊C₃

156 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 1140

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 371);