C₃×C₇⋊#95 #10620588

order	672
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₇ ⋊ #95
Sylow	C₇ ⋊ C₃×#95

152 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 672

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 170);