C₂×C₁₇² #10596805

order	578
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 78336
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₇

Aliases

C₂×C₁₇²

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 578

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19);(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(578, 5);