Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7827 |
358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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) = 13568 |
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)(56,61)(59,60)(62,65)(63,68)(64,70)(66,72)(67,73)(69,75)(71,77)(74,76)(78,81,83,82)(79,85,86,90)(80,88,89,91)(84,92,93,87);(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)(62,64,66,71)(63,67,69,74)(65,70,72,77)(68,73,75,76)(78,80)(79,84)(81,88)(82,91)(83,89)(85,92)(86,93)(87,90);(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)(54,55,57,60)(56,58,61,59)(62,63,66,69)(64,67,71,74)(65,68,72,75)(70,76,77,73)(78,79,83,86)(80,87,89,92)(81,85,82,90)(84,91,93,88)Polycyclic presentation:
2^8,53|a^2=fgh,b^2=g,c^2=f,d^2=f,e^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,i^a=i^52,d^b=df,e^b=eg,i^b=i^52,d^c=dg,e^c=eh1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 58857);