C₉×C₇⋊C₈ #92578

order	504
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = C₂³×C₃×AGL(1,𝔽₇) (order 1008) · Inn(G) = D₇ · Out(G) = C₂³×C₃²
homology	Abelianization (H₁) = C₈×C₉ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₇ ⋊ C₈×C₉
Hall	C₇×C₉ ⋊ C₈

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 2 generators on 24 points:

(2,3)(4,5)(6,7)(8,9,10,12,11,13,14,15)(16,17,19,18,20,22,21,23,24);(1,2,4,6,7,5,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 4);