C₂×C₇×D₁₁×C₁₉⋊C₃ #31798265

order	17556
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₁₁×C₁₉⋊C₃
unambiguous semidirect product	C₁₁⋊(C₂²×C₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₁₁)⋊(C₂×C₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₁₉×D₁₁)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₁×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₇

80 conjugacy classes of subgroups.

μ_t(G) = 2926

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 80);