C₃×D₃×C₅⋊(D₂₉⋊C₇) #49141402

order	36540
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×D₃×C₅⋊(D₂₉⋊C₇)
unambiguous semidirect product	(C₅×D₃)⋊(C₃×D₂₉⋊C₇)
unambiguous semidirect product	(D₃×C₂₉⋊C₇)⋊(C₃×D₅)
unambiguous semidirect product	(D₃×D₁₄₅)⋊(C₃×C₇)
unambiguous semidirect product	(C₃×D₃×D₁₄₅)⋊C₇

	subgroup	G/H
center, hypercenter	C₃	D₃×C₅⋊(D₂₉⋊C₇)
commutator, cosocle, hypocenter	C₃×C₅×C₂₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₂₉	C₂²×C₇
LCS	G ▷ C₃×C₅×C₂₉
UCS	C₁ ◁ C₃

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 870

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 244);