Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#20276320 |
| Sylow | C53 ⋊ C2×#2110 |
738 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)(58,67)(62,75)(66,81)(68,70)(69,83)(74,84)(76,77)(82,85);(56,58)(57,62,64,75)(59,70)(60,69)(61,67)(63,77,78,76)(65,66,80,81)(68,72)(71,74)(73,83)(79,85,87,82)(84,86);(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)(56,57,59,63,60,65,71,79,61,64,72,78,73,80,86,87)(58,66,68,82,69,75,84,77,67,81,70,85,83,62,74,76);(54,55)2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322226);