C₇×#168 #63296

order	280
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂³×C₃×AGL(1,𝔽₅) (order 480) · Inn(G) = D₅ · Out(G) = C₂⁴×C₃
homology	Abelianization (H₁) = C₇×C₈ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₅ ⋊ C₇×C₈
Hall	C₅×C₇ ⋊ C₈

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 280

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 1);