D₃×C₇×C₂₉×D₁₅ #49141604

order	36540
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×C₂₉×D₁₅
unambiguous semidirect product	(C₃×D₃)⋊(C₇×D₅×C₂₉)
unambiguous semidirect product	(C₅×D₃)⋊(D₃×C₇×C₂₉)

	subgroup	G/H
center, hypercenter	C₇×C₂₉	D₃×D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₇×C₂₉

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 6090

5481 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 446);