Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #12559 |
554 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)(86,98)(91,105)(97,111)(99,113)(100,114)(101,115)(106,108)(107,112);(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)(80,81,82,83)(84,86,89,101,88,100,103,113,90,98,104,115,102,114,87,99)(85,91,94,107,95,108,110,111,96,105,109,112,93,106,92,97);(84,85,88,93,90,96,102,95)(86,97,100,112,98,111,114,107)(87,94,89,92,103,109,104,110)(91,101,106,113,105,115,108,99)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,d^2=gh,e^2=h,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,c^b=ch,i^b=i^782248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84457);