Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C4×C8 |
No aliases for this group.
| Sylow | C53 ⋊ #8137 |
354 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 155 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:
(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)(62,65,66,76,67,77,78,89)(63,69,70,81,71,82,83,91)(64,73,74,86,75,87,88,93)(68,79,72,84,80,90,85,92);(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)(62,64)(63,68,71,80)(65,73)(66,74)(67,75)(69,79,82,90)(70,72,83,85)(76,86)(77,87)(78,88)(81,84,91,92)(89,93);(54,55,56,58,57,59,60,61)(62,63)(64,72,75,85)(65,69)(66,70)(67,71)(68,74,80,88)(73,84,87,92)(76,81)(77,82)(78,83)(79,86,90,93)(89,91)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=d,d^2=g,e^2=h,b^a=bd,f^a=fg,e^b=eg,i^c=i^521232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 60006);