Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #12668 |
308 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)(80,83,98,84,87,99,86,85)(81,89,105,90,92,106,93,91)(82,95,96,100,97,111,102,101)(88,94,104,107,103,110,109,108);(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)(81,88,92,103)(83,95)(84,100)(85,101)(86,102)(87,97)(89,94,106,110)(90,107,91,108)(93,109,105,104)(96,98)(99,111);(80,81,85,91,86,93,99,106,87,92,84,90,98,105,83,89)(82,94,95,104,96,107,100,103,97,110,111,109,102,108,101,88)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,g^2=h,b^a=bd,f^a=fh,d^b=dg,e^b=egh,g^b=gh,i^b=i^783184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84947);