Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#20275235 |
| Sylow | C53 ⋊ C2×#1909 |
1686 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)(57,63)(58,67)(60,74)(61,72)(62,76)(64,79)(65,70)(66,80)(68,84)(69,83)(71,75)(73,78)(77,86)(81,87)(82,85);(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)(56,58,60,68,61,69,75,85)(57,62,64,66,65,77,73,81)(59,67,74,84,72,83,71,82)(63,76,79,80,70,86,78,87);(56,57)(58,66)(59,70,72,63)(60,73)(61,65)(62,68)(64,75)(67,80,83,87)(69,81)(71,78,74,79)(76,82,86,84)(77,85);(54,55)1202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 171539);