Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#15690911 |
| Fitting | C4×C97 ⋊ C32 |
| Sylow | C97 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 388 |
A minimal faithful permutation representation — 2 generators on 101 points:
(1,2,8,28,49,94,92,83,4,17,51,95,42,40,86,89,24,59,43,74,73,60,6,22,61,91,88,14,3,13,9,25,54,19,11,36,38,82,39,85,87,64,32,76,26,70,10,34,79,90,18,33,77,69,66,75,23,65,46,84,62,67,57,35,5,20,55,31,41,12,37,80,47,81,52,21,56,29,30,15,44,68,97,96,71,78,53,58,50,16,45,48,63,93,72,27,7)(98,99,100,101);(2,3,4,9,5,10,14,29,6,11,15,30,18,32,42,70,7,12,16,31,19,33,37,73,21,35,43,74,34,75,78,77)(8,23,24,62,25,63,66,65,26,41,67,84,28,71,61,45,27,64,68,82,55,94,76,87,69,13,38,39,72,40,81,83)(17,46,47,56,48,88,90,86,49,89,54,22,57,58,95,59,50,85,91,60,92,80,79,96,93,97,20,52,36,51,53,44)(99,101)Polycyclic presentation:
2^7,97|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^28,h^d=h^8,h^e=h^64,h^f=h^22,h^g=h^9692 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21812);