Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1334 ⋊ C2 |
| Sylow | C53 ⋊ #11600 |
386 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 105 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)(62,65,67,79)(63,69,72,71)(64,74,76,77)(66,78,82,93)(68,83,84,85)(70,86,88,80)(73,87,89,90)(75,91,92,81);(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)(62,64,67,76)(63,68,72,84)(65,77,79,74)(66,81,82,91)(69,85,71,83)(70,87,88,90)(73,80,89,86)(75,78,92,93);(54,55,56,58,57,59,60,61)(62,63)(64,73,76,89)(65,69)(66,80)(67,72)(68,75,84,92)(70,78)(71,79)(74,87,77,90)(81,83,91,85)(82,86)(88,93)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,c^b=ch,d^b=dfh,e^b=eh,f^b=fh,i^c=i^52896 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79345);