SO⁺(4,𝔽₃) #10596400

order	576
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂×C₃

Aliases

SO⁺(4,𝔽₃)

Fitting	H(5,𝔽₂) ⋊ C₃⋊D₃
derived	Ω⁺(4,𝔽₃) ⋊ C₂

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂	A₄⋊S₄
commutator, cosocle, hypocenter	Ω⁺(4,𝔽₃)	C₂
Fitting	H(5,𝔽₂)	C₃⋊D₃
LCS	G ▷ Ω⁺(4,𝔽₃)
UCS	C₁ ◁ C₂

127 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 24

Polycyclic presentation:

2,3^2,2^5|d^2=h,e^2=h,f^2=h,g^2=h,b^a=b^2,c^a=c^2,d^a=eh,e^a=dh,f^a=gh,g^a=fh,f^b=fg,g^b=f,d^c=de,e^c=d,e^d=eh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8282);