Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #28138 |
860 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 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)(55,59)(58,60)(64,74)(69,84)(73,89)(75,76)(78,90)(83,92)(85,91)(86,93);(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)(62,65,68,81)(63,70,72,87)(64,73,74,89)(66,80,67,79)(69,83,84,92)(71,88,82,77)(75,78,76,90)(85,93,91,86);(54,56,57,61)(55,58,59,60)(62,64,67,76,68,74,66,75)(63,69,71,85,72,84,82,91)(65,78,80,89,81,90,79,73)(70,86,77,92,87,93,88,83);(54,55)(56,60)(57,59)(58,61)(62,63)(64,69)(65,77)(66,82)(67,71)(68,72)(70,79)(73,86)(74,84)(75,91)(76,85)(78,92)(80,87)(81,88)(83,90)(89,93)Polycyclic presentation:
2^8,53|b^2=eg,c^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,c^b=cg,d^b=dh,f^c=fh,g^c=gh,i^c=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 257487);