Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #8485 |
630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 127 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)(80,82,84,89)(81,86,87,95)(83,91,92,88)(85,93,90,94)(96,99)(97,103)(98,107)(100,114)(101,111)(102,116)(104,110)(105,121)(106,122)(108,123)(109,125)(112,115)(113,124)(117,127)(118,119)(120,126);(80,81)(82,86)(83,90)(84,87)(85,92)(88,93)(89,95)(91,94)(96,98)(97,102)(99,107)(100,113)(101,108)(103,116)(104,106)(105,120)(109,115)(110,122)(111,123)(112,125)(114,124)(117,119)(118,127)(121,126);(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)(81,85,87,90)(86,94,95,93)(96,97,100,105,101,104,115,119)(98,106,109,120,108,102,113,117)(99,110,112,121,111,103,114,118)(107,122,124,127,123,116,125,126)Polycyclic presentation:
2^8,79|a^2=f,c^2=h,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^78,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,f^c=fg1519 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 61881);