Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D53×#1905 |
| Fitting | C53×#1905 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1905 |
1678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,4,7,21)(2,9,12,25)(3,14,17,30)(5,20,6,19)(8,22,23,32)(10,18,11,24)(13,27,26,31)(15,29,16,28)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,3)(2,8,12,23)(4,14)(5,15)(6,16)(7,17)(9,22,25,32)(10,13,11,26)(18,27,24,31)(19,28)(20,29)(21,30);(1,2,6,10,7,12,5,11)(3,13,16,23,17,26,15,8)(4,18,20,9,21,24,19,25)(14,22,29,31,30,32,28,27);(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171454);