Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C4×C97 ⋊ C8 |
| Sylow | C97 ⋊ #1850 |
348 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 776 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,7,18,40,69,82,96,87,51,84,27,57,88,42,71,62,32,61,65,64,33,5,13,35,56,86,80,45,73,66,15,30,3,10,25,54,85,92,90,95,75,22,48,16,39,46,9,20,44,11,26,55,36,63,21,47,76,89,93,97,77,53,24,4,12,14,38,67,23,49,81,29,59,34,8,19,43,72,78,31,60,91,41,70,79,28,58,50,83,94,52,74,68,37,17,6)(103,105);(2,4,5,11,6,3,8,9)(7,15,16,18,17,14,36,37)(10,22,23,26,24,21,45,46)(12,28,29,44,30,27,56,20)(13,32,33,41,34,31,19,42)(25,51,52,40,53,50,82,68)(35,60,48,54,59,62,63,77)(38,64,65,55,66,43,72,39)(47,74,67,70,75,69,73,88)(49,61,79,87,80,78,57,83)(58,90,81,91,84,89,86,71)(76,93,94,85,95,92,96,97)(99,101);(2,3,5,9,6,4,8,11)(7,14,16,37,17,15,36,18)(10,21,23,46,24,22,45,26)(12,27,29,20,30,28,56,44)(13,31,33,42,34,32,19,41)(25,50,52,68,53,51,82,40)(35,62,48,77,59,60,63,54)(38,43,65,39,66,64,72,55)(47,69,67,88,75,74,73,70)(49,78,79,83,80,61,57,87)(58,89,81,71,84,90,86,91)(76,92,94,97,95,93,96,85)(98,99)(100,101)(102,103)(104,105)Polycyclic presentation:
2^7,97|a^2=f,b^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^33,h^b=h^64,h^f=h^22,h^g=h^96176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21655);