Finite Group DatabasebetaFinite Group Databasebeta| order | 16807 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C49 · Schur multiplier (H2) = C73 |
| direct product | C7×C49⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C73 | C72 |
| commutator | C7 | C72×C49 |
| Frattini, cosocle | C72 | C73 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C73 ◁ G | |
| LECS | G ▷ C72 ▷ C1 | |
426 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 16807 |
A minimal faithful permutation representation — 3 generators on 105 points:
(1,2,3,4,5,6,7);(9,11,14,19,27,39,49)(12,16,22,31,15,20,28)(17,24,34,23,32,21,29)(25,36,30,40,33,42,35)(37,46,44,41,50,45,43)(47,56,55,54,53,52,51)(57,58,60,63,67,72,78,59,61,64,68,73,79,85,62,65,69,74,80,86,91,66,70,75,81,87,92,96,71,76,82,88,93,97,100,77,83,89,94,98,101,103,84,90,95,99,102,104,105);(8,9,12,17,25,37,47,10,11,15,21,30,41,51,13,14,16,23,33,43,52,18,19,20,24,35,44,53,26,27,22,29,36,45,54,38,39,28,32,40,46,55,48,49,31,34,42,50,56)2695 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16807, 49);