D₃×C₇×D₅×C₁₃⋊C₃ #30655485

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×D₅×C₁₃⋊C₃
unambiguous semidirect product	(C₅×D₃)⋊(C₂×C₇×C₁₃⋊C₃)
unambiguous semidirect product	(C₃×D₅)⋊(C₂×C₇×C₁₃⋊C₃)
unambiguous semidirect product	D₁₅⋊(C₂×C₇×C₁₃⋊C₃)
unambiguous semidirect product	(D₃×D₅×C₁₃)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₇	D₃×D₅×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₃×C₅×C₁₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₃	C₂²×C₃
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁ ◁ C₇

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 1365

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 535);