#1443⋊C₃ #68009

order	384
isoclinism	isoclinic class of #396⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Fitting, Sylow	#1443 ⋊ C₃
derived	#95 ⋊ C₃×C₄

111 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 16 points:

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

Polycyclic presentation:

2,3,2^6|a^2=cfg,d^2=fg,e^2=f,d^a=dfh,e^a=eg,c^b=cg,d^b=eg,e^b=defgh,f^b=gh,g^b=fgh,e^d=eh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 585);