Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #12079 |
204 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 119 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)(80,82,83,85,84,86,87,81)(89,96,98,109)(91,106)(95,111,113,112)(97,115,116,104)(99,117,118,114)(100,119)(105,110)(107,108);(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)(88,90,94,103)(89,95,98,113)(91,105,106,110)(92,102,93,101)(96,111,109,112)(97,114,116,117)(99,104,118,115)(100,108,119,107);(80,81,83,82,84,85,87,86)(88,89,92,96,94,98,93,109)(90,99,101,117,103,118,102,114)(91,104,107,116,106,115,108,97)(95,110,112,100,113,105,111,119)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=ef,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cfg,d^a=df,f^a=fh,d^b=dfh,e^b=eh,f^b=fh,i^b=i^78,d^c=dh1288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81531);