C₂×C₂₃×C₁₆₉⋊C₃ #37552211

order	23322
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₃×C₁₆₉⋊C₃
unambiguous semidirect product	(C₂×C₁₆₉)⋊(C₃×C₂₃)
unambiguous semidirect product	(C₂×C₂₃×C₁₆₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₂₃	C₁₆₉⋊C₃
commutator, cosocle, hypocenter	C₁₆₉	C₂×C₃×C₂₃
Frattini	C₁₃	C₂×C₂₃×C₁₃⋊C₃
Fitting	C₂×C₂₃×C₁₆₉	C₃
socle	C₂×C₁₃×C₂₃	C₁₃⋊C₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₂×C₂₃

24 conjugacy classes of subgroups.

μ_t(G) = 7774

2714 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23322, 5);