Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C8×C16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #12518 |
330 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 99 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:
(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)(54,55,59,61,57,60,56,58)(63,69)(68,81)(70,83)(71,80)(72,84)(77,92)(82,85)(86,91);(62,64,73,87,67,76,79,90,66,75,88,93,78,89,65,74)(63,68,77,86,71,82,83,84,69,81,92,91,80,85,70,72);(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)(56,59)(60,61)(62,63)(64,72)(65,77)(66,69)(67,80)(68,74)(70,73)(71,78)(75,84)(76,91)(79,92)(81,90)(82,93)(83,88)(85,87)(86,89)Polycyclic presentation:
2^8,53|b^2=df,c^2=egh,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,i^a=i^523398 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84291);