Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1362 ⋊ C2 |
| Sylow | C53 ⋊ #11953 |
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 points:
(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)(54,57,59,58)(55,61,62,63)(56,65,66,67)(60,68,64,69)(71,78)(77,93)(79,80)(81,96)(82,94)(95,101)(97,99)(98,100);(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)(54,56)(55,60)(57,65)(58,67)(59,66)(61,68)(62,64)(63,69)(70,72,76,86)(71,77,78,93)(73,87,74,90)(75,92,88,85)(79,97,80,99)(81,101,96,95)(82,100,94,98)(83,91,84,89);(54,55,58,63,59,62,57,61)(56,64,65,69,66,60,67,68)(70,71,74,80,88,96,89,98,76,78,73,79,75,81,91,100)(72,82,84,95,92,99,87,77,86,94,83,101,85,97,90,93)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=f,d^2=gh,e^2=fgh,g^2=h,b^a=bd,c^a=ch,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^c=i^52800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80920);