C₂²×C₃⁴×C₄ #13049765

order	1296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4658135040
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃⁶

Aliases

C₂²×C₃⁴×C₄

5724 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 1296

A minimal faithful permutation representation — 4 generators on 20 points:

(1,2,3,4)(9,10,11);(5,6)(12,13,14);(7,8)(15,16,17);(18,19,20)

1296 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 3483);