C₁₉×Dic₅ #67409

order	380
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂²×C₉×AGL(1,𝔽₅) (order 720) · Inn(G) = D₅ · Out(G) = C₂³×C₉
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×Dic₅

derived, Sylow	C₅ ⋊ C₄×C₁₉
Hall	C₅×C₁₉ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 380

A minimal faithful permutation representation — 2 generators on 28 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);(20,22,21,23)(25,28)(26,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(380, 1);