Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1785 ⋊ C2 |
| Sylow | C53 ⋊ #8539 |
1008 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 115 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 — 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)(63,69)(64,72)(66,76)(67,75)(68,78)(70,82)(71,81)(73,85)(74,86)(77,88)(79,84)(80,90)(83,92)(87,89)(91,93);(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)(54,56)(55,58)(57,61)(59,60)(62,64)(63,68)(65,72)(66,74)(67,73)(69,78)(70,80)(71,79)(75,85)(76,86)(77,87)(81,84)(82,90)(83,91)(88,89)(92,93);(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)(56,60,61,58)(57,59)(62,63,66,70,67,71,77,83)(64,68,74,80,73,79,87,91)(65,69,76,82,75,81,88,92)(72,84,86,93,85,78,89,90)Polycyclic presentation:
2^8,53|a^2=f,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^52,e^b=eh,f^b=fg,i^b=i^52,d^c=dh872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 62165);