(PSU(3,𝔽₂)⋊C₉)⋊C₂ #13049174

order	1296
isoclinism	isoclinic class of (PSU(3,𝔽₂)⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	PSU(3,𝔽₂)⋊C₉	C₂
Frattini	C₃	AGL(2,𝔽₃)
Fitting, socle	C₃³	GL(2,𝔽₃)
LCS	G ▷ PSU(3,𝔽₂)⋊C₉
UCS	C₁

73 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 72

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2892);