C₃×#6489 #10621237

order	672
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₇ ⋊ #117
Sylow	C₇ ⋊ C₃×#117

152 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 22 points:

(1,2,3)(4,5,7,9,10,8,6)(16,20)(19,22);(15,17,18,21)(16,19,20,22);(5,6)(7,8)(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, 819);