Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #12881 |
298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(80,82,83,81)(85,92,93,94)(88,103)(91,105,96,106)(95,110,109,108)(98,102)(101,104)(107,115,111,114)(112,113);(80,81,83,82)(84,86,87,97,90,100,89,99)(85,91,94,106,93,96,92,105)(88,102,101,113,103,98,104,112)(95,111,110,114,109,107,108,115);(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)(81,82)(84,85,88,95,89,92,104,108,90,93,103,109,87,94,101,110)(86,96,98,111,99,106,113,115,100,91,102,107,97,105,112,114)Polycyclic presentation:
2^8,79|a^2=f,b^2=e,c^2=d,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^78,f^b=fh,f^c=fh3184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85922);