Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#20273492 |
| Fitting | C2×C53×#334 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1572 |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6784 |
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)(58,64)(61,67)(65,70)(68,71)(72,75,77,76)(73,79,80,85)(74,82,84,83)(78,81,86,87);(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)(57,61)(59,65)(60,64)(62,68)(63,67)(66,70)(69,71)(72,74,76,83,77,84,75,82)(73,78,79,81,80,86,85,87);(56,57,59,62,60,63,66,69)(58,61,65,68,64,67,70,71)(72,73)(74,81)(75,79)(76,85)(77,80)(78,83)(82,86)(84,87);(54,55)1532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 138632);