C₂×C₃×C₇×C₁₃×D₁₅ #30655790

order	16380
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₃	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₃	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃×C₇×C₁₃

176 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

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

μ_t(G) = 5460

4914 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 840);