C₇×C₉⋊C₁₆ #11758832

order	1008
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₇×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉⋊C₁₆
unambiguous semidirect product	C₉⋊(C₇×C₁₆)

derived, Sylow	C₉ ⋊ C₇×C₁₆
Hall	C₇×C₉ ⋊ C₁₆

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1008

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7)(9,11)(10,14)(12,13)(15,16)(17,18,19,22,20,23,25,28,21,24,26,29,27,30,31,32);(8,16,11,14,13,12,10,9,15)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 3);