Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20276835 |
| Fitting | C2×C53×#504 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2221 |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 87 points:
(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)(57,65)(59,70)(60,74)(61,69)(62,71)(63,75)(64,79)(66,83)(67,81)(68,82)(72,85)(73,84)(76,87)(77,80)(78,86);(56,57,64,77,61,67,73,78,62,68,72,76,60,66,59,63)(58,65,79,80,69,81,84,86,71,82,85,87,74,83,70,75);(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)(57,63)(58,69)(59,64)(60,61)(65,80)(66,77)(67,76)(68,78)(70,84)(71,74)(72,73)(75,81)(82,87)(83,86);(54,55)2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 324125);