C₆₁×D₁₉₉ #37566314

order	24278
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₁×D₁₉₉
unambiguous semidirect product	C₁₉₉⋊(C₂×C₆₁)

Fitting, socle, Hall	C₆₁×C₁₉₉ ⋊ C₂
derived, Sylow	C₁₉₉ ⋊ C₂×C₆₁

	subgroup	G/H
center, hypercenter	C₆₁	D₁₉₉
commutator, cosocle, hypocenter	C₁₉₉	C₂×C₆₁
Frattini	C₁	G
Fitting, socle	C₆₁×C₁₉₉	C₂
LCS	G ▷ C₁₉₉
UCS	C₁ ◁ C₆₁

8 conjugacy classes of subgroups.

μ_t(G) = 12139

6161 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24278, 2);