C₄×C₇² #5996

order	196
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×#10621462 (order 4032) · Inn(G) = C₁ · Out(G) = C₂×C₃×#10621462
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₄×C₇²

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 196

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(196, 7);