Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #11573 |
358 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 358 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) = 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)(54,57,59,58)(55,61,63,62)(56,64,65,66)(60,67,68,69);(54,56)(55,60)(57,66)(58,64)(59,65)(61,69)(62,67)(63,68)(71,75,78,76)(73,81)(77,83,85,84)(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)(54,55,58,62,59,63,57,61)(56,60,64,67,65,68,66,69)(70,71,73,77,74,78,81,85)(72,75,79,83,80,76,82,84)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=gh,d^2=h,e^2=g,b^a=bd,d^a=df,f^a=fh,i^a=i^52,c^b=cgh,e^b=efh,e^d=eh1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79233);