C₂×C₅×C₃₇ #67306

order	370
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₄²×C₉ (order 144) · Inn(G) = C₁ · Out(G) = C₄²×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₇₀
abelian	C₂×C₅×C₃₇

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 370

A minimal faithful permutation representation — 1 generator on 44 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(370, 4);