C₂×C₁₉×C₁₉₃⋊C₃ #36347303

order	22002
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×C₁₉₃⋊C₃
unambiguous semidirect product	(C₂×C₁₉₃)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₁₉₃⋊C₃
commutator, cosocle, hypocenter	C₁₉₃	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₁₉₃	C₃
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₂×C₁₉

16 conjugacy classes of subgroups.

μ_t(G) = 7334

2546 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22002, 2);