Q₈×#6891 #14517836

order	1944
nilpotency class	2
isoclinism	isoclinic class of D₄×C₃²⋊H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃³ · Schur multiplier (H₂) = C₃³

Aliases

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂×C₃²	C₂²×C₃³
prime radical	C₂×C₃⁴	C₂²×C₃
LCS	G ▷ C₂×C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ G

756 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3,4)(5,8,7,6)(9,10,12,11,14,16,15,13,17)(18,19,21)(20,23,25)(22,26,24);(1,5,3,7)(2,6,4,8)(10,13,14)(12,16,17);(19,22,23)(21,25,26)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2230);