Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12401 |
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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)(55,61)(57,58)(60,68)(62,63)(64,69)(65,66)(70,73,76,75)(71,78,80,90)(72,82,84,91)(74,88,89,85)(77,93,94,95)(79,97,98,86)(81,96,99,100)(83,101,92,87);(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)(54,56,59,67)(55,60,63,69)(57,66,58,65)(61,68,62,64)(70,72,76,84)(71,77,80,94)(73,82,75,91)(74,87,89,101)(78,93,90,95)(79,96,98,100)(81,97,99,86)(83,85,92,88);(54,55,59,63)(56,64,67,68)(57,62,58,61)(60,66,69,65)(70,71,76,80)(72,81,84,99)(73,78,75,90)(74,86,89,97)(77,92,94,83)(79,85,98,88)(82,100,91,96)(87,93,101,95)Polycyclic presentation:
2^8,53|a^2=g,b^2=g,c^2=h,d^2=fh,e^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=egh,f^a=fh,d^b=df,e^b=eg,f^b=fh,i^b=i^52,d^c=dg,e^c=egh629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 83577);