Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#20274767 |
| Sylow | C53 ⋊ C2×#1814 |
1330 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)(56,59)(57,64)(58,68)(60,73)(61,76)(62,74)(63,77)(65,79)(66,80)(67,81)(69,83)(70,85)(71,84)(72,75)(78,87)(82,86);(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)(56,58,60,69,62,71,61,70)(57,63,65,67,66,78,75,82)(59,68,73,83,74,84,76,85)(64,77,79,81,80,87,72,86);(56,57)(58,67)(59,72,74,79)(60,75)(61,65)(62,66)(63,69)(64,73,80,76)(68,77,84,87)(70,78)(71,82)(81,83,86,85);(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, 169228);