Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #7177 |
238 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 115 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) = 10112 |
A minimal faithful permutation representation — 2 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)(80,82,84,87,85,86,83,81)(88,90,93,104,111,103,110,102,94,106,109,118,92,105,91,108)(89,95,98,114,97,117,112,101,100,115,107,119,99,113,96,116);(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)(80,81,83,86,85,87,84,82)(88,89,92,97,94,100,111,99)(90,101,103,114,106,116,105,119)(91,107,109,96,110,98,93,112)(95,104,113,102,115,118,117,108)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,i^a=i^78,c^b=ch,d^b=dh3184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56501);