C₃×C₇⋊C₃₂ #10620422

order	672
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₇ ⋊ C₃×C₃₂
Hall	C₃×C₇ ⋊ C₃₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 672

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12,13,17,14,18,21,27,15,19,22,28,24,30,33,37,16,20,23,29,25,31,34,38,26,32,35,39,36,40,41,42);(4,5,7,9,10,8,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 4);