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×#1368 ⋊ C2 |
| Sylow | C53 ⋊ #11999 |
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 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:
(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)(63,70,72,82)(64,74,76,77)(66,78,81,80)(69,83,84,93)(71,79,85,92)(73,86,87,91)(75,88,89,90);(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)(62,64,66,75,67,77,80,90,68,76,81,89,65,74,78,88)(63,69,71,73,70,83,79,86,72,84,85,87,82,93,92,91);(54,55,56,58,57,59,60,61)(62,63)(64,73,76,87)(65,70)(66,79)(67,82)(68,72)(69,75,84,89)(71,80)(74,86,77,91)(78,85)(81,92)(83,88,93,90)Polycyclic presentation:
2^8,53|a^2=e,b^2=d,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,e^b=eh,i^c=i^52896 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81121);