D₅²×C₃₄₉ #46853145

order	34900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃₄₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅²×C₃₄₉
unambiguous semidirect product	(C₅×D₅)⋊(C₂×C₃₄₉)
unambiguous semidirect product	(C₅⋊D₅)⋊(C₂×C₃₄₉)

Fitting, socle, Hall	C₅²×C₃₄₉ ⋊ C₂²
derived, Sylow	C₅² ⋊ C₂²×C₃₄₉

	subgroup	G/H
center, hypercenter	C₃₄₉	D₅²
commutator, cosocle, hypocenter	C₅²	C₂²×C₃₄₉
Frattini	C₁	G
Fitting, socle	C₅²×C₃₄₉	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₄₉

48 conjugacy classes of subgroups.

μ_t(G) = 3490

5584 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34900, 34);