C₁₃×D₃₅⋊D₉ #30655159

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

Aliases

direct product	C₁₃×D₃₅⋊D₉
unambiguous semidirect product	D₃₅⋊(C₁₃×D₉)
unambiguous semidirect product	D₄₅⋊(C₁₃×D₇)
unambiguous semidirect product	D₆₃⋊(D₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	D₃₅⋊D₉
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₁₃
Frattini	C₃	C₁₃×D₁₅⋊D₇
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 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) = 4095

1248 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 209);