C₅⋊D₅×C₆₄₁ #44545337

order	32050
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₄₁ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅⋊D₅×C₆₄₁
unambiguous semidirect product	C₅⋊(D₅×C₆₄₁)

Fitting, socle, Hall	C₅²×C₆₄₁ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₆₄₁

	subgroup	G/H
center, hypercenter	C₆₄₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₆₄₁
Frattini	C₁	G
Fitting, socle	C₅²×C₆₄₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₆₄₁

32 conjugacy classes of subgroups.

μ_t(G) = 16025

8974 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32050, 15);