Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C97 ⋊ C8 |
| Sylow | C97 ⋊ #1278 |
172 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 55 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 — 2 generators on 105 points:
(1,2,12,50,95,83,27,10)(3,8,28,49,94,96,87,42)(4,14,59,25,51,35,6,22)(5,11,29,37,64,80,77,53)(7,21,61,91,89,71,15,20)(9,13,55,66,90,60,23,26)(16,38,84,81,65,88,43,47)(17,19,52,33,85,41,70,74)(18,39,44,73,67,72,32,54)(24,48,62,46,69,31,36,86)(30,34,79,82,92,97,75,78)(40,45,76,93,63,68,56,57)(99,102,104,103);(2,3,5,9,7,10,6,4)(8,15,17,29,19,20,18,16)(11,23,24,28,26,27,25,12)(13,30,32,53,33,35,14,31)(21,40,42,46,44,22,43,41)(34,56,47,74,58,52,38,57)(36,60,37,62,51,72,61,54)(39,63,65,45,67,71,66,64)(48,75,76,86,77,83,50,55)(49,79,78,87,81,59,70,80)(68,89,85,84,88,73,82,69)(90,96,95,91,94,93,92,97)(98,99)(100,102)(101,104)(103,105)Polycyclic presentation:
2^7,97|a^2=d,b^2=e,c^2=f,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^47,h^b=h^64,h^d=h^75,h^e=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, 21517);