Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #12904 |
318 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)(80,81,82,83)(85,91)(90,103)(92,105)(93,102)(94,106)(98,112)(104,114)(107,111);(84,86,87,95,89,97,100,109,88,96,99,108,101,110,113,115)(85,90,92,94,93,104,98,107,91,103,105,106,102,114,112,111);(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)(81,83)(84,85)(86,94,96,106)(87,98)(88,91)(89,102)(90,95,103,108)(92,100)(93,101)(97,111,110,107)(99,112)(104,115,114,109)(105,113)Polycyclic presentation:
2^8,79|a^2=f,b^2=d,c^2=eh,d^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^78,f^b=fh3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85998);