C₂×C₃⋊(C₁₇⋊(D₄₉⋊C₃)) #44472437

order	29988
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃⋊(C₁₇⋊(D₄₉⋊C₃))
unambiguous semidirect product	(C₂×C₃)⋊(C₁₇⋊(D₄₉⋊C₃))
unambiguous semidirect product	(C₂×C₁₇)⋊(C₃⋊(D₄₉⋊C₃))
unambiguous semidirect product	(C₂×C₄₉⋊C₃)⋊D₅₁
unambiguous semidirect product	(C₂×D₂₄₉₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₁₇⋊(D₄₉⋊C₃))
commutator, cosocle, hypocenter	C₃×C₁₇×C₄₉	C₂²×C₃
Frattini	C₇	C₂×C₃⋊(C₁₇⋊AGL(1,𝔽₇))
Fitting	C₂×C₃×C₁₇×C₄₉	C₂×C₃
socle	C₂×C₃×C₇×C₁₇	AGL(1,𝔽₇)
LCS	G ▷ C₃×C₁₇×C₄₉
UCS	C₁ ◁ C₂

132 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.

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

μ_t(G) = 4998

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 78);