Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#20276508 |
| Fitting | C2×C53×#368 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2161 |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(58,69)(63,78)(67,81)(70,85)(71,72)(77,84)(79,82)(83,86);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,58,68,84,61,72,75,85,62,69,74,77,60,71,59,70)(57,63,73,83,65,79,80,81,66,78,87,86,76,82,64,67);(56,57,60,65,62,66,61,76)(58,67,71,83,69,81,72,86)(59,73,74,80,75,87,68,64)(63,77,79,85,78,84,82,70);(54,55)1208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322622);