Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #8861 |
420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 127 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)(55,58)(56,61)(59,60)(62,64,66,74,67,73,77,87)(63,68,70,80,71,79,83,91)(65,72,76,86,75,85,88,89)(69,78,82,90,81,84,92,93);(54,55)(56,58)(57,60)(59,61)(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,b^2=f,d^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,d^b=dg,e^b=eh,i^b=i^52,d^c=dh1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 63587);