Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #12792 |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
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)(80,83)(81,89)(82,95)(84,99)(85,103)(86,100)(87,102)(88,104)(90,98)(91,108)(92,109)(93,107)(94,110)(96,101)(97,106)(105,111);(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)(80,82,84,96,87,97,86,85)(81,88,90,94,93,92,91,105)(83,95,99,101,102,106,100,103)(89,104,98,110,107,109,108,111);(80,81,85,92,86,90,97,105,87,93,96,88,84,91,82,94)(83,98,101,110,100,107,95,109,102,108,103,111,99,89,106,104)Polycyclic presentation:
2^8,79|a^2=f,b^2=d,d^2=h,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^b=i^78,e^c=eh,f^c=fh1780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85524);