#49154262

order	37503
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

C₄₆₃ ⋊ #733

	subgroup	G/H
center	C₃	C₃²⋊(C₄₆₃⋊C₃)
commutator, prime radical, cosocle	C₃²×C₄₆₃	C₃²
Frattini	C₃²	C₃×C₄₆₃⋊C₃
Fitting	3₋¹⁺²×C₄₆₃	C₃
socle	C₃×C₄₆₃	H(3,𝔽₃)
hypercenter	3₋¹⁺²	C₄₆₃⋊C₃
hypocenter	C₄₆₃	#733
LCS	G ▷ C₃²×C₄₆₃ ▷ C₃×C₄₆₃ ▷ C₄₆₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ 3₋¹⁺²

26 conjugacy classes of subgroups.

μ_t(G) = 12501

Polycyclic presentation:

3^4,463|a^3=d,b^3=d^2,b^a=bc,c^a=cd,e^b=e^21

1711 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37503, 36);