C₅×C₇² #6927

order	245
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₃×C₄×#10621462 (order 8064) · Inn(G) = C₁ · Out(G) = C₃×C₄×#10621462
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₅×C₇²

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 245

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(245, 2);