Q₈×#6855 #14516250

order	1944
nilpotency class	2
isoclinism	isoclinic class of D₄×H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉² · Schur multiplier (H₂) = C₃³

Aliases

	subgroup	G/H
center, Frattini, socle, prime radical, cosocle	C₂×C₃³	C₂²×C₃²
commutator	C₂×C₃	C₂²×C₉²
LCS	G ▷ C₂×C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ G

414 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1944

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4)(5,8,7,6)(9,10,12)(11,14,16)(13,17,15)(18,19,21,20,22,24,23,25,26);(1,5,3,7)(2,6,4,8)(10,13,14)(12,16,17)(27,28,30,29,31,33,32,34,35)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 644);