D₁₁²×C₆₁ #44443254

order	29524
automorphism	?
homology	Abelianization (H₁) = C₂²×C₆₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₁₁²×C₆₁
unambiguous semidirect product	(C₁₁×D₁₁)⋊(C₂×C₆₁)
unambiguous semidirect product	(C₁₁⋊D₁₁)⋊(C₂×C₆₁)

Fitting, socle, Hall	C₁₁²×C₆₁ ⋊ C₂²
derived, Sylow	C₁₁² ⋊ C₂²×C₆₁

	subgroup	G/H
center, hypercenter	C₆₁	D₁₁²
commutator, cosocle, hypocenter	C₁₁²	C₂²×C₆₁
Frattini	C₁	G
Fitting, socle	C₁₁²×C₆₁	C₂²
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₆₁

60 conjugacy classes of subgroups.

μ_t(G) = 1342

2989 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29524, 25);