Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#1822 ⋊ C2 |
| Sylow | C53 ⋊ #23953 |
1166 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 175 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 — 4 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)(55,59)(58,60)(62,66,68,67)(63,71,72,80)(64,74,75,81)(65,77,79,78)(69,83,85,84)(70,76,87,88)(73,90,91,92)(82,93,86,89);(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)(62,65,68,79)(63,70,72,87)(64,73,75,91)(66,78,67,77)(69,82,85,86)(71,88,80,76)(74,92,81,90)(83,89,84,93);(54,56,57,61)(55,58,59,60)(62,64)(63,69)(65,73)(66,74)(67,81)(68,75)(70,86)(71,83)(72,85)(76,89)(77,90)(78,92)(79,91)(80,84)(82,87)(88,93);(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)(56,60)(57,59)(58,61)(62,63)(64,69)(65,76)(66,71)(67,80)(68,72)(70,78)(73,89)(74,83)(75,85)(77,87)(79,88)(81,84)(82,90)(86,92)(91,93)Polycyclic presentation:
2^8,53|b^2=e,c^2=h,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^52,c^b=cg,f^b=fh,d^c=dh,f^c=fh,i^c=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 201639);