#1839⋊C₃ #68028

order	384
isoclinism	isoclinic class of #126⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Sylow	#1839 ⋊ C₃
derived	C₄² ⋊ C₃×C₈

60 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 24 points:

(1,7,22,10,3,19,6,18,21,9,15,23,5,11,20,8,14,16,4,17,12,2,13,24);(1,6,5,4)(2,8,9,10)(3,14)(12,22,21,20)(13,15)(16,24,19,23)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 604);