#10624527⋊C₂ #13090576

order	1458
isoclinism	isoclinic class of #6883⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₃

Aliases

Fitting, Sylow	#10624527 ⋊ C₂
derived	#732 ⋊ C₂×C₉

97 conjugacy classes of subgroups.

μ_t(G) = 54

Polycyclic presentation:

2,3^6|b^3=e,d^3=g^2,b^a=bc,c^a=c^2,d^a=d^2g,e^a=eg^2,f^a=fg,g^a=g^2,c^b=cd,d^b=df,f^b=fg,d^c=dfg,f^c=fg

maximal subgroup of	#72222260, #72222296
maximal normal subgroup of	#72222296

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 650);