Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #13616 |
302 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 89 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)(59,65)(64,77)(66,79)(67,76)(69,85)(73,89)(78,81)(80,88);(58,59)(60,69)(61,73)(62,76)(63,65)(64,68)(66,70)(67,74)(71,88)(72,85)(75,89)(77,84)(78,87)(79,86)(80,82)(81,83);(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)(59,64)(60,68)(61,70)(62,74)(65,77)(66,80)(67,81)(69,73)(71,87)(72,84)(75,86)(76,78)(79,88)(82,83)(85,89)Polycyclic presentation:
2^8,53|a^2=e,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^52,c^b=ch,d^b=df,f^b=fg,g^b=gh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90007);