C₅⋊D₅×C₄₃₁ #36340668

order	21550
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₃₁ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅⋊D₅×C₄₃₁
unambiguous semidirect product	C₅⋊(D₅×C₄₃₁)

Fitting, socle, Hall	C₅²×C₄₃₁ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₄₃₁

	subgroup	G/H
center, hypercenter	C₄₃₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₄₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₄₃₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄₃₁

32 conjugacy classes of subgroups.

μ_t(G) = 10775

6034 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21550, 15);