D₃×C₁₃×D₄₉⋊C₃ #37524207

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₁₃×D₄₉⋊C₃
unambiguous semidirect product	D₄₉⋊(C₃×D₃×C₁₃)
unambiguous semidirect product	(D₃×D₄₉)⋊(C₃×C₁₃)
unambiguous semidirect product	(C₃×D₄₉⋊C₃)⋊(C₂×C₁₃)
unambiguous semidirect product	(D₃×C₄₉⋊C₃)⋊(C₂×C₁₃)
unambiguous semidirect product	(C₃⋊(D₄₉⋊C₃))⋊(C₂×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	D₃×D₄₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₄₉	C₂²×C₃×C₁₃
Frattini	C₇	D₃×C₁₃×AGL(1,𝔽₇)
Fitting	C₃×C₁₃×C₄₉	C₂²×C₃
socle	C₃×C₇×C₁₃	C₂×AGL(1,𝔽₇)
LCS	G ▷ C₃×C₄₉
UCS	C₁ ◁ C₁₃

132 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 1911

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 152);