C₂₉×C₃⋊(ΓL(1,𝔽₈)⋊AGL(1,𝔽₅)) #49141466

order	36540
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×C₃⋊(ΓL(1,𝔽₈)⋊AGL(1,𝔽₅))
unambiguous semidirect product	C₃⋊(C₂₉×ΓL(1,𝔽₈)⋊AGL(1,𝔽₅))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂₉×ΓL(1,𝔽₁₆))
unambiguous semidirect product	(C₃⋊(C₇⋊AGL(1,𝔽₅)))⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂₉×C₃⋊(C₇⋊AGL(1,𝔽₅)))⋊C₃

112 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 3045

1131 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 308);