Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1360 ⋊ C2 |
| Sylow | C53 ⋊ #11924 |
414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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 — 3 generators on 93 points:
(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)(62,65,68,67)(63,70,73,72)(64,75,77,78)(66,79,83,82)(69,84,85,86)(71,80,89,88)(74,87,90,91)(76,92,93,81);(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)(55,58)(56,60)(62,64)(63,69)(65,75)(66,81)(67,78)(68,77)(70,84)(71,87)(72,86)(73,85)(74,88)(76,79)(80,90)(82,93)(83,92)(89,91);(54,55,56,59,57,58,60,61)(62,63)(64,74,77,90)(65,70)(66,80)(67,72)(68,73)(69,76,85,93)(71,82)(75,87,78,91)(79,89)(81,84,92,86)(83,88)Polycyclic presentation:
2^8,53|a^2=e,c^2=h,d^2=gh,e^2=fg,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^c=i^52812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 80790);