D₅×(C₁₃⋊C₉)⋊D₇ #30655073

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×(C₁₃⋊C₉)⋊D₇
unambiguous semidirect product	(D₅×C₁₃⋊C₉)⋊D₇

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×(C₁₃⋊C₃)⋊D₇
commutator, hypocenter	C₅×C₇×C₁₃	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅×C₇×C₁₃	C₂²×C₃
prime radical	C₃×D₅×D₉₁	C₃
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₃

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 123);