Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #17782 |
1244 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 323 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) = 3392 |
A minimal faithful permutation representation — 4 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)(62,66,68,64)(63,71,72,73)(65,74,67,75)(69,76,77,70);(62,65,68,67)(63,70,72,76)(64,74,66,75)(69,71,77,73);(55,58)(56,60)(62,64,68,66)(63,69,72,77)(65,74,67,75)(70,71,76,73);(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)(65,70)(66,71)(67,76)(68,72)(69,74)(75,77)Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=h,d^2=h,e^2=h,f^2=gh,b^a=be,e^a=eg,i^a=i^52,e^b=eh,f^b=fgh,d^c=dh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 138530);