D₅×D₁₁×C₄₉⋊C₃ #44568360

order	32340
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×D₁₁×C₄₉⋊C₃
unambiguous semidirect product	(D₅×C₁₁)⋊(C₂×C₄₉⋊C₃)
unambiguous semidirect product	(C₅×D₁₁)⋊(C₂×C₄₉⋊C₃)
unambiguous semidirect product	D₅₅⋊(C₂×C₄₉⋊C₃)
unambiguous semidirect product	(D₅×D₁₁×C₄₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₁₁×C₄₉	C₂²×C₃
Frattini	C₇	D₅×ΓL(1,𝔽₈)×D₁₁
socle	C₅×C₇×C₁₁	C₂²×ΓL(1,𝔽₈)
LCS	G ▷ C₅×C₁₁×C₄₉
UCS	C₁

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

normal subgroups only

This group has 120 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) = 2695

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 62);