C₇×C₃⋊C₃₂ #10620421

order	672
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₇×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₃⋊C₃₂
unambiguous semidirect product	C₃⋊(C₇×C₃₂)

derived, Sylow	C₃ ⋊ C₇×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:

(1,2,3,4,5,6,7)(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);(8,9,10)

336 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 3);