Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #30250 |
966 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 966 conjugacy classes of subgroups — too many to draw. Only its 219 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) = 6784 |
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)(60,64)(63,65)(66,69,71,70)(67,73,74,78)(68,76,77,79)(72,80,81,75);(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)(55,57)(58,60)(59,63)(61,64)(62,65)(66,68,71,77)(67,72,74,81)(69,76,70,79)(73,80,78,75);(54,55,56,57)(59,62)(63,65);(58,59)(60,63)(61,62)(64,65)(66,67,70,73,71,74,69,78)(68,75,76,81,77,80,79,72)Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=h,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^c=de,f^c=fh,i^c=i^521496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 281815);