C₂×#444 #2954

order	128
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) = #72235124 (order 2048) · Inn(G) = C₂×D₄ · Out(G) = #3484
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

232 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 4 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1686);