#1842⋊C₃ #68030

order	384
isoclinism	isoclinic class of #127⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₄

Aliases

Fitting, Sylow	#1842 ⋊ C₃
derived	C₄² ⋊ C₃×C₈

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3,5,4,6,7,8)(9,10,13,12,14,17)(11,20,18)(15,19,16);(9,11,12,16)(10,15,14,20)(13,17)(18,19)

Polycyclic presentation:

2,3,2^6|a^2=c,c^2=d,e^2=g,f^2=h,b^a=bg,e^a=eg,f^a=fh,e^b=efh,f^b=egh,g^b=gh,h^b=g

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 606);