Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#20273070 |
| Sylow | C53 ⋊ C2×#1470 |
1002 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)(56,59,60,67)(57,62,63,69)(58,65,66,71)(61,68,64,70)(74,80)(77,83)(81,86)(84,87);(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)(56,58,60,66)(57,61,63,64)(59,65,67,71)(62,68,69,70)(72,74)(73,77)(75,81)(76,80)(78,84)(79,83)(82,86)(85,87);(56,57)(58,64,66,61)(59,62)(60,63)(65,70,71,68)(67,69)(72,73,75,78,76,79,82,85)(74,77,81,84,80,83,86,87);(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, 135521);