C₁₁²×C₆₁⋊C₅ #49147236

order	36905
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₁² · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₁₁²×C₆₁⋊C₅
unambiguous semidirect product	C₆₁⋊(C₅×C₁₁²)

Fitting, socle, Hall	C₁₁²×C₆₁ ⋊ C₅
derived, Sylow	C₆₁ ⋊ C₅×C₁₁²

	subgroup	G/H
center, hypercenter	C₁₁²	C₆₁⋊C₅
commutator, cosocle, hypocenter	C₆₁	C₅×C₁₁²
Frattini	C₁	G
Fitting, socle	C₁₁²×C₆₁	C₅
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₁₁²

56 conjugacy classes of subgroups.

μ_t(G) = 7381

2057 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36905, 9);