D₅×D₂₉×C₇⋊C₉ #49141237

order	36540
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×D₂₉×C₇⋊C₉
unambiguous semidirect product	(D₅×C₂₉)⋊(C₂×C₇⋊C₉)
unambiguous semidirect product	(C₅×D₂₉)⋊(C₂×C₇⋊C₉)
unambiguous semidirect product	D₁₄₅⋊(C₂×C₇⋊C₉)
unambiguous semidirect product	(C₇×D₅×D₂₉)⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×ΓL(1,𝔽₈)×D₂₉
commutator, hypocenter	C₅×C₇×C₂₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅×C₇×C₂₉	C₂²×C₃
prime radical	C₃×C₇×D₅×D₂₉	C₃
LCS	G ▷ C₅×C₇×C₂₉
UCS	C₁ ◁ C₃

120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 9135

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 79);