C₂×C₃⁴×C₇ #11765824

order	1134
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 145566720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃⁶

Aliases

C₂×C₃⁴×C₇

848 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1134

A minimal faithful permutation representation — 4 generators on 21 points:

(1,2)(3,4,5)(15,16,17,18,19,20,21);(6,7,8);(9,10,11);(12,13,14)

1134 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 254);