Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13471 |
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 115 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(81,83)(84,87,92,86)(85,94,98,93)(88,103,89,106)(90,101,100,102)(91,104,109,107)(95,112,110,114)(96,99,108,105)(97,113,111,115);(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,86,100,106,91,104,89,102,92,87,90,103,109,107,88,101)(85,93,108,114,97,113,110,105,98,94,96,112,111,115,95,99);(84,85,91,111,92,98,109,97)(86,99,104,112,87,105,107,114)(88,108,100,95,89,96,90,110)(93,106,115,102,94,103,113,101)Polycyclic presentation:
2^8,79|a^2=de,b^2=dg,c^2=h,d^2=gh,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,c^b=cf,i^b=i^78,d^c=dg,e^c=eg,f^c=fgh,g^c=gh1288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89296);