C₅×D₃×C₁₃×D₂₁ #30655717

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

Aliases

direct product	C₅×D₃×C₁₃×D₂₁
unambiguous semidirect product	(C₃×D₃)⋊(C₅×C₁₃×D₇)
unambiguous semidirect product	(D₃×C₇)⋊(C₅×D₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₃×D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₃	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₅×C₁₃

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 2730

2340 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 767);