C₂²×C₄×C₁₁² #14515561

order	1936
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2534400
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₁₁

Aliases

C₂²×C₄×C₁₁²

378 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1936

A minimal faithful permutation representation — 3 generators on 30 points:

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

1936 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1936, 155);