Q₈×#6900 #14517845

order	1944
nilpotency class	2
isoclinism	isoclinic class of D₄×C₃²⋊H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃³ · Schur multiplier (H₂) = C₃

Aliases

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

420 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 648

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2239);