Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#2163 ⋊ C2 |
| Sylow | C53 ⋊ #11946 |
302 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 95 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:
(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)(54,57,59,58)(55,61,62,63)(56,65,66,67)(60,68,64,69)(71,77)(76,91)(78,79)(80,93)(81,99)(92,98)(94,96)(95,97);(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)(55,60)(57,65)(58,67)(59,66)(61,68)(62,64)(63,69)(70,72)(71,76)(73,86)(74,84)(75,90)(77,91)(78,94)(79,96)(80,98)(81,95)(82,89)(83,100)(85,87)(88,101)(92,93)(97,99);(54,55,58,63,59,62,57,61)(56,64,65,69,66,60,67,68)(70,71,73,79,87,93,100,95,74,77,88,78,75,80,89,97)(72,81,83,98,90,96,86,91,84,99,82,92,85,94,101,76)Polycyclic presentation:
2^8,53|a^2=e,c^2=fh,d^2=gh,e^2=fg,g^2=h,b^a=bd,c^a=ch,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^b=i^521502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80886);