Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#3549 ⋊ C2 |
| Sylow | C53 ⋊ #33559 |
1248 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1248 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 848 |
A minimal faithful permutation representation — 4 generators on 69 points:
(1,3,5,9)(2,7,8,15)(4,10,11,16)(6,12,13,14)(17,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19);(3,9)(4,11)(7,15)(12,14);(2,6)(3,9)(7,14)(8,13)(10,16)(12,15);(1,2)(3,7)(4,6)(5,8)(9,15)(10,12)(11,13)(14,16)(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)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)Polycyclic presentation:
2^8,53|d^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^52,d^b=dh,f^b=fgh,d^c=dh,e^c=eg,f^e=fh1022 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323700);