Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#2163 ⋊ C2 |
| Sylow | C53 ⋊ #11491 |
356 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 103 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:
(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)(62,65,66,81,68,82,69,67)(63,71,83,73,74,80,72,90)(64,76,84,93,79,85,77,78)(70,86,75,87,88,91,89,92);(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)(55,58)(56,60)(62,64)(63,70)(65,76)(66,84)(67,78)(68,79)(69,77)(71,86)(72,89)(73,87)(74,88)(75,83)(80,91)(81,93)(82,85)(90,92);(54,55,56,59,57,58,60,61)(62,63,67,73,69,72,82,71,68,74,81,90,66,83,65,80)(64,75,78,91,77,70,85,87,79,89,93,86,84,88,76,92)Polycyclic presentation:
2^8,53|a^2=e,c^2=fg,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=ch,d^a=df,d^b=dh,e^b=efh,i^b=i^521508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78897);