C₅×C₁₃×D₇×D₉ #30655127

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₁₃×D₇×D₉
unambiguous semidirect product	(C₇×D₉)⋊(C₂×C₅×C₁₃)
unambiguous semidirect product	(C₉×D₇)⋊(C₂×C₅×C₁₃)
unambiguous semidirect product	D₆₃⋊(C₂×C₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₇×D₉
commutator, cosocle, hypocenter	C₇×C₉	C₂²×C₅×C₁₃
Frattini	C₃	C₅×D₃×C₁₃×D₇
Fitting	C₅×C₇×C₉×C₁₃	C₂²
socle	C₃×C₅×C₇×C₁₃	C₂×D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₅×C₁₃

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

normal subgroups only

This group has 120 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) = 4095

1950 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 177);