Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11817 |
386 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 79 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) = 3392 |
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)(56,64)(61,62)(65,66)(71,76)(75,83)(77,84)(78,85);(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)(55,59,60,69)(57,66)(58,64)(61,68,62,63)(65,67)(70,72)(71,75)(73,81)(74,80)(76,83)(77,85)(78,84)(79,82);(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)(54,55,57,62,58,60,67,61)(56,63,66,59,64,68,65,69)(70,71)(72,78,80,85)(73,77)(74,76)(75,79,83,81)(82,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,d^2=gh,e^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^52,c^b=ch,d^b=dg,e^b=efgh,i^b=i^52,e^d=eh860 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80317);