Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12872 |
398 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 131 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) = 3392 |
A minimal faithful permutation representation — 3 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)(54,56,57,60)(55,59,58,61)(63,69)(65,78)(66,81)(68,82)(70,71)(72,87)(73,77)(74,89)(75,92)(79,80)(83,84)(85,93)(86,88)(90,91);(55,58)(59,61)(62,64,67,76)(63,68,73,86)(65,74,80,91)(66,75,81,92)(69,82,77,88)(70,83,87,93)(71,84,72,85)(78,89,79,90);(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)(56,59)(57,58)(60,61)(62,63,66,71,67,73,81,72)(64,68,75,84,76,86,92,85)(65,77,79,70,80,69,78,87)(74,88,90,83,91,82,89,93)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=d,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,e^c=egh,f^c=fh,g^c=gh1502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85881);