Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #33728 |
482 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 93 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)(62,65,68,67)(63,70,72,82)(64,76,74,78)(66,79,81,75)(69,84,83,88)(71,80,85,93)(73,87,86,92)(77,91,89,90);(62,64,75,90,67,78,81,89,68,74,79,91,65,76,66,77)(63,69,80,87,70,84,85,86,72,83,93,92,82,88,71,73);(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)(54,56,57,61)(55,58,59,60)(64,74)(69,83)(73,86)(76,78)(77,89)(84,88)(87,92)(90,91);(54,55,57,59)(56,60,61,58)(62,63)(64,73)(65,70)(66,80)(67,82)(68,72)(69,77)(71,75)(74,86)(76,87)(78,92)(79,85)(81,93)(83,89)(84,91)(88,90)Polycyclic presentation:
2^8,53|a^2=e,b^2=e,c^2=fg,d^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,c^b=ch,i^b=i^521196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 325069);