C₁₃×D₉×D₃₅ #30655155

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×D₉×D₃₅
unambiguous semidirect product	(C₅×D₉)⋊(C₁₃×D₇)
unambiguous semidirect product	(C₇×D₉)⋊(D₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	D₉×D₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₁₃
Frattini	C₃	D₃×C₁₃×D₃₅
Fitting	C₅×C₇×C₉×C₁₃	C₂²
socle	C₃×C₅×C₇×C₁₃	C₂×D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₁₃

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

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

μ_t(G) = 4095

1482 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 205);