Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11976 |
292 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 85 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)(55,60)(59,62)(61,68)(67,69)(70,73,76,75)(71,72,78,81)(74,82,84,79)(77,80,83,85);(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)(54,56,58,64)(55,59,60,62)(57,65,66,63)(61,69,68,67)(70,72)(71,75)(73,78)(74,83)(76,81)(77,84)(79,80)(82,85);(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)(54,55,57,61,58,60,66,68)(56,62,63,69,64,59,65,67)(70,71,74,77,73,81,82,85,76,78,84,83,75,72,79,80)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=h,d^2=gh,e^2=fgh,g^2=h,b^a=bd,c^a=cfh,d^a=df,i^a=i^52,d^b=dg,e^b=efg,g^b=gh,i^b=i^521184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81021);