C₂⁴×C₁₁² #14515573

order	1936
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 266112000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₁₁

Aliases

C₂⁴×C₁₁²

938 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 30 points:

(1,2)(9,10,11,12,13,14,15,16,17,18,19);(3,4)(20,21,22,23,24,25,26,27,28,29,30);(5,6);(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, 167);