C₅×C₁₃×D₉×D₁₃ #44477744

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₁₃×D₉×D₁₃
unambiguous semidirect product	(C₁₃×D₉)⋊(C₂×C₅×C₁₃)
unambiguous semidirect product	(C₉×D₁₃)⋊(C₂×C₅×C₁₃)
unambiguous semidirect product	D₁₁₇⋊(C₂×C₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₉×D₁₃
commutator, cosocle, hypocenter	C₉×C₁₃	C₂²×C₅×C₁₃
Frattini	C₃	C₅×D₃×C₁₃×D₁₃
Fitting	C₅×C₉×C₁₃²	C₂²
socle	C₃×C₅×C₁₃²	C₂×D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₅×C₁₃

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

normal subgroups only

This group has 192 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) = 1170

3120 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 333);