C₅×D₃×C₃₄₉⋊C₃ #44536116

order	31410
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃×C₃₄₉⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₅×C₃₄₉⋊C₃)
unambiguous semidirect product	(D₃×C₃₄₉)⋊(C₃×C₅)
unambiguous semidirect product	(C₅×D₃×C₃₄₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₅	D₃×C₃₄₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₃₄₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₄₉	C₂×C₃
LCS	G ▷ C₃×C₃₄₉
UCS	C₁ ◁ C₅

36 conjugacy classes of subgroups.

μ_t(G) = 5235

1785 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31410, 18);