Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #11297 |
578 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)(81,83)(84,87,88,102,90,104,89,103)(85,92,93,108,95,109,94,101)(86,97,98,112,100,113,99,114)(91,105,96,110,107,111,106,115);(80,81)(82,83)(84,86,88,99,90,100,89,98)(85,91,93,106,95,107,94,96)(87,97,103,112,104,113,102,114)(92,105,101,110,109,111,108,115);(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)(84,85,89,94,90,95,88,93)(86,96,99,91,100,106,98,107)(87,101,102,92,104,108,103,109)(97,111,112,115,113,105,114,110)Polycyclic presentation:
2^8,79|a^2=g,b^2=e,c^2=d,d^2=h,e^2=h,g^2=h,b^a=bd,c^a=ce,i^a=i^78,c^b=cf,d^b=dh,f^b=fh,g^b=gh,e^c=eh,f^c=fh,g^c=gh1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 78011);