Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13855 |
1246 conjugacy classes of subgroups; only the 427 normal subgroups are shown.
This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 427 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 81 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)(74,76,77,80)(75,79,78,81);(59,63)(62,65)(66,68,69,73)(67,71,70,72)(75,78)(79,81);(58,60,61,64)(59,62,63,65)(67,70)(71,72)(74,75)(76,79)(77,78)(80,81);(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)(54,55,56,57)(58,59)(60,62)(61,63)(64,65)(66,67)(68,72)(69,70)(71,73)Polycyclic presentation:
2^8,53|a^2=h,b^2=ef,c^2=e,d^2=g,b^a=be,c^a=cf,i^a=i^52,c^b=cg2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 91347);