Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1362 ⋊ C2 |
| Sylow | C79 ⋊ #11953 |
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 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) = 127 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 127 points:
(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)(80,83,85,84)(81,87,88,89)(82,91,92,93)(86,94,90,95)(97,104)(103,119)(105,106)(107,122)(108,120)(121,127)(123,125)(124,126);(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)(81,86)(83,91)(84,93)(85,92)(87,94)(88,90)(89,95)(96,98,102,112)(97,103,104,119)(99,113,100,116)(101,118,114,111)(105,123,106,125)(107,127,122,121)(108,126,120,124)(109,117,110,115);(80,81,84,89,85,88,83,87)(82,90,91,95,92,86,93,94)(96,97,100,106,114,122,115,124,102,104,99,105,101,107,117,126)(98,108,110,121,118,125,113,103,112,120,109,127,111,123,116,119)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=f,d^2=gh,e^2=fgh,g^2=h,b^a=bd,c^a=ch,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^c=i^781177 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 80920);