(#1020⋊C₃)⋊C₂ #10596772

order	576
isoclinism	isoclinic class of (#1020⋊C₃)⋊C₂
automorphism	Aut(G) = #10596770⋊C₂ (order 1152) · Inn(G) = G · Out(G) = C₂
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂²

Aliases

Fitting, socle	C₂⁴ ⋊ D₃²
derived	A₄² ⋊ C₂²

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	A₄²	C₂²
Fitting, socle	C₂⁴	D₃²
LCS	G ▷ A₄²
UCS	C₁

128 conjugacy classes of subgroups.

minimal degree	μ(G) = 8
transitive degree	μ_t(G) = 8

Polycyclic presentation:

2^2,3^2,2^4|c^a=c^2,d^a=d^2,e^a=f,f^a=e,g^a=h,h^a=g,c^b=cd,d^b=d^2,e^b=g,f^b=h,g^b=e,h^b=f,g^c=h,h^c=gh,e^d=f,f^d=ef,g^d=gh,h^d=g

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8654);