Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20276116 |
| Sylow | C53 ⋊ C2×#2070 |
950 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)(56,59,61,73)(57,64,66,80)(58,68,70,71)(60,75,62,72)(63,77,78,87)(65,81,74,79)(67,82,83,86)(69,85,76,84);(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)(56,58,60,69,61,70,62,76)(57,63,65,67,66,78,74,83)(59,71,72,85,73,68,75,84)(64,77,79,86,80,87,81,82);(56,57,62,65,61,66,60,74)(58,67,76,78,70,83,69,63)(59,64,75,79,73,80,72,81)(68,82,85,77,71,86,84,87);(54,55)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 198289);