Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #12450 |
206 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 67 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) = 20224 |
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)(96,98,99,107)(97,103,102,117)(100,113,110,127)(101,116,111,109)(104,120,118,126)(105,121,115,119)(106,123,122,112)(108,125,124,114);(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)(80,82,89,93,84,91,83,90)(81,85,92,95,87,94,86,88)(97,102)(103,117)(104,118)(105,115)(106,122)(112,123)(119,121)(120,126);(80,81,84,87)(82,88,91,95)(83,92,89,86)(85,93,94,90)(96,97)(98,106)(99,102)(100,112)(101,115)(103,108)(104,114)(105,111)(107,122)(109,126)(110,123)(113,121)(116,120)(117,124)(118,125)(119,127)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfh,c^2=h,d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,e^c=eg,g^c=gh,i^c=i^781525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 83883);