Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7292 |
198 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 91 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 — 2 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)(54,56)(55,59,61,62)(57,64)(58,63)(60,67,68,69)(65,66)(70,71,73,78,74,79,82,85,75,77,72,76,81,83,80,84);(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)(54,55,57,60,58,61,65,68)(56,62,64,69,63,59,66,67)(71,76,77,78)(72,80)(73,82)(74,81)(79,85,83,84)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=f,d^2=g,e^2=f,f^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fh,i^a=i^52,c^b=cg,d^b=dh1502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56804);