Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #10628 |
292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 292 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) = 119 |
| transitive degree | μt(G) = 5056 |
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)(81,84)(82,87)(85,86)(88,91,92,103,93,104,106,117)(89,95,96,109,97,110,112,119)(90,99,100,115,101,102,105,116)(94,107,98,113,108,118,111,114);(80,81,83,86)(82,84,87,85)(88,90)(89,94)(91,102)(92,105)(93,101)(95,107)(96,111)(97,108)(98,112)(99,104)(100,106)(103,115)(109,114)(110,118)(113,119)(116,117);(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)(88,89)(90,98,101,111)(91,95)(92,96)(93,97)(94,100,108,105)(99,114,102,113)(103,109)(104,110)(106,112)(107,116,118,115)(117,119)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=d,d^2=g,f^2=h,b^a=bd,c^a=ce,f^a=fg,i^a=i^78,c^b=cf,d^b=dg,e^b=eg,f^b=fh,f^c=fgh1522 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 74344);