C₂×C₃×D₅×C₃₄₉ #35230287

order	20940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₃₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×D₅×C₃₄₉
unambiguous semidirect product	C₅⋊(C₂²×C₃×C₃₄₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃×C₃₄₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₃₄₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₃₄₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₃₄₉

40 conjugacy classes of subgroups.

μ_t(G) = 10470

8376 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20940, 47);