C₇×#830 #10620628

order	672
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₈ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₇ ⋊ C₂²⋊C₈
Sylow	C₃ ⋊ C₇×C₂²⋊C₈

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 336

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 210);