C₇×C₁₃×C₃⋊D₃×D₁₁ #49114972

order	36036
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₇×C₁₃×C₃⋊D₃×D₁₁
unambiguous semidirect product	(C₃×D₁₁)⋊(D₃×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₇×C₁₃	C₃⋊D₃×D₁₁
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂²
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₇×C₁₃

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

normal subgroups only

This group has 240 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) = 9009

3822 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 640);