C₆₁×D₂₅₁ #44499528

order	30622
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₁×D₂₅₁
unambiguous semidirect product	C₂₅₁⋊(C₂×C₆₁)

Fitting, socle, Hall	C₆₁×C₂₅₁ ⋊ C₂
derived, Sylow	C₂₅₁ ⋊ C₂×C₆₁

	subgroup	G/H
center, hypercenter	C₆₁	D₂₅₁
commutator, cosocle, hypocenter	C₂₅₁	C₂×C₆₁
Frattini	C₁	G
Fitting, socle	C₆₁×C₂₅₁	C₂
LCS	G ▷ C₂₅₁
UCS	C₁ ◁ C₆₁

8 conjugacy classes of subgroups.

μ_t(G) = 15311

7747 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30622, 2);