Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #8689 |
346 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 111 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)(80,82,83,89)(81,86,85,94)(84,93,91,90)(87,95,92,88)(96,99)(97,102)(98,106)(100,110)(101,104)(103,109)(105,108)(107,111);(81,85)(86,94)(87,92)(88,95)(96,98,101,108,102,109,100,107)(97,103,110,111,99,106,104,105);(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)(82,88)(83,85)(84,92)(86,90)(87,91)(89,95)(93,94)(96,97,101,104,102,99,100,110)(98,105,108,106,109,111,107,103)Polycyclic presentation:
2^8,79|a^2=f,b^2=dgh,c^2=h,d^2=g,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,e^c=egh,f^c=fg2230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62847);