Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12021 |
216 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 115 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)(55,58)(59,61)(62,65,68,67)(63,70,72,82)(64,74,76,77)(66,78,81,80)(69,83,84,85)(71,79,86,93)(73,87,88,89)(75,90,91,92);(62,64,66,75,67,74,80,90,68,76,81,91,65,77,78,92)(63,69,71,73,70,85,79,89,72,84,86,88,82,83,93,87);(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)(54,55,56,59,57,58,60,61)(62,63)(64,73,76,88)(65,70)(66,79)(67,82)(68,72)(69,75,84,91)(71,80)(74,87,77,89)(78,86)(81,93)(83,90,85,92)Polycyclic presentation:
2^8,53|a^2=e,b^2=d,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^52,c^b=ch,e^b=eh2132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81207);