C₂×C₁₃×C₃⋊D₃×C₅₉ #42120282

order	27612
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃×C₅₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₁₃×C₃⋊D₃×C₅₉
unambiguous semidirect product	(C₂×C₃)⋊(D₃×C₁₃×C₅₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₅₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₅₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₃×C₅₉

120 conjugacy classes of subgroups.

μ_t(G) = 13806

9204 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27612, 126);