C₃×C₄⋊(C₇⋊C₈) #10620561

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

Aliases

direct product	C₃×C₄⋊(C₇⋊C₈)
unambiguous semidirect product	C₄⋊(C₃×C₇⋊C₈)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 143);