C₂×C₁₃² #66765

order	338
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 26208
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₃

Aliases

C₂×C₁₃²

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 338

A minimal faithful permutation representation — 2 generators on 28 points:

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

338 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(338, 5);