Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#20273423 |
| Sylow | C53 ⋊ C2×#1554 |
974 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6784 |
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)(56,59,61,60)(57,63,64,68)(58,66,67,69)(62,70,65,71)(73,78)(77,86)(79,83)(80,87);(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)(56,58,61,67)(57,62,64,65)(59,66,60,69)(63,70,68,71)(72,74,76,82)(73,77,78,86)(75,84,85,81)(79,87,83,80);(56,57,60,63,61,64,59,68)(58,65,66,70,67,62,69,71)(72,73)(74,80)(75,83)(76,78)(77,81)(79,85)(82,87)(84,86);(54,55)2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 137949);