C₅⋊D₅×C₄₁₉ #35230324

order	20950
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₁₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅⋊D₅×C₄₁₉
unambiguous semidirect product	C₅⋊(D₅×C₄₁₉)

Fitting, socle, Hall	C₅²×C₄₁₉ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₄₁₉

	subgroup	G/H
center, hypercenter	C₄₁₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₄₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₄₁₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄₁₉

32 conjugacy classes of subgroups.

μ_t(G) = 10475

5866 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20950, 9);