C₂₉×D₃₅⋊D₉ #49141301

order	36540
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₉×D₃₅⋊D₉
unambiguous semidirect product	D₃₅⋊(D₉×C₂₉)
unambiguous semidirect product	D₄₅⋊(D₇×C₂₉)
unambiguous semidirect product	D₆₃⋊(D₅×C₂₉)

	subgroup	G/H
center, hypercenter	C₂₉	D₃₅⋊D₉
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₂₉
Frattini	C₃	C₂₉×D₁₅⋊D₇
Fitting	C₅×C₇×C₉×C₂₉	C₂²
socle	C₃×C₅×C₇×C₂₉	C₂×D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₂₉

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) = 9135

2784 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 143);