Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#2183 ⋊ C2 |
| Sylow | C53 ⋊ #12049 |
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 77 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)(62,64,66,71,67,72,74,77,65,63,68,69,73,70,75,76);(54,55,57,59)(56,61,60,58)(63,64)(69,71)(70,72)(76,77);(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)(56,60)(59,61)(62,63,66,69,67,70,74,76,65,64,68,71,73,72,75,77)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,i^a=i^52,c^b=ch,d^b=df1532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 81341);