Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C53 ⋊ #12593 |
338 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 195 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)(62,65,66,82,69,83,68,67)(63,71,72,89,74,90,75,73)(64,77,78,79,81,93,80,84)(70,85,76,86,87,92,88,91);(62,64)(63,70,74,87)(65,77)(66,78)(67,84)(68,80)(69,81)(71,85,90,92)(72,76,75,88)(73,91,89,86)(79,82)(83,93);(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)(54,55,56,58,57,59,60,61)(62,63,67,73,68,75,83,90,69,74,82,89,66,72,65,71)(64,76,79,92,80,70,77,86,81,88,84,85,78,87,93,91)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=d,d^2=h,e^2=g,g^2=h,b^a=bd,f^a=fh,i^a=i^52,e^b=eh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84577);