C₇×#625 #92682

order	504
isoclinism	isoclinic class of #625
automorphism	Aut(G) = C₂×C₃×#64241 (order 1728) · Inn(G) = D₃² · Out(G) = C₂×C₃×D₄
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃²×C₇ ⋊ D₄
Sylow	C₃² ⋊ C₇×D₄

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 108);