C₂×C₃×C₅×C₃₄₉⋊C₃ #44536119

order	31410
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₅ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×C₅×C₃₄₉⋊C₃
unambiguous semidirect product	(C₂×C₃₄₉)⋊(C₃²×C₅)
unambiguous semidirect product	(C₂×C₃×C₃₄₉)⋊(C₃×C₅)
unambiguous semidirect product	(C₂×C₅×C₃₄₉)⋊C₃²
unambiguous semidirect product	(C₂×C₃×C₅×C₃₄₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	C₃₄₉⋊C₃
commutator, cosocle, hypocenter	C₃₄₉	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₃₄₉	C₃
LCS	G ▷ C₃₄₉
UCS	C₁ ◁ C₂×C₃×C₅

48 conjugacy classes of subgroups.

μ_t(G) = 10470

3570 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31410, 21);