C₄⋊(#126⋊C₃) #73219

order	384
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

unambiguous semidirect product	C₄⋊(#126⋊C₃)
unambiguous semidirect product	#2860⋊C₃

126 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:

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

Polycyclic presentation:

2^2,3,2^5|b^2=d,e^2=gh,f^2=g,b^a=bd,c^a=ch,e^a=eg,f^a=fh,e^c=fgh,f^c=ef,g^c=h,h^c=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5795);