C₃×Dic₇⋊C₈ #10620571

order	672
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃×C₇ ⋊ C₄⋊C₈
Sylow	C₇ ⋊ C₃×C₄⋊C₈

76 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)(12,14)(15,16,17,19,18,20,21,22);(5,6)(7,8)(9,10)(11,12,13,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 153);