Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #8348 |
726 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 135 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)(64,73)(66,77)(67,76)(68,80)(70,83)(71,82)(72,86)(74,87)(75,88)(78,90)(79,89)(81,91)(84,93)(85,92);(54,55)(56,60)(57,59)(58,61)(62,64)(63,68)(65,73)(66,78)(67,74)(69,80)(70,72)(71,85)(75,79)(76,87)(77,90)(81,84)(82,92)(83,86)(88,89)(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)(55,58,59,60)(62,63,66,71,67,70,79,84)(64,72,75,85,74,68,78,81)(65,69,77,82,76,83,89,93)(73,80,88,91,87,86,90,92)Polycyclic presentation:
2^8,53|a^2=f,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=i^52,d^b=dh,e^b=eg,f^b=fgh,d^c=dg1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61089);