Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #11320 |
546 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)(84,87,88,101,89,102,95,110)(85,91,92,107,93,99,104,113)(86,96,97,111,98,100,103,115)(90,105,94,109,106,112,108,114);(84,86,95,97,89,98,88,103)(85,90,104,94,93,106,92,108)(87,100,110,115,102,96,101,111)(91,105,113,109,99,112,107,114);(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)(84,85)(86,94,98,108)(87,99)(88,92)(89,93)(90,97,106,103)(91,102)(95,104)(96,109,100,114)(101,113)(105,111,112,115)(107,110)Polycyclic presentation:
2^8,79|a^2=g,b^2=de,c^2=d,d^2=h,b^a=bd,c^a=ce,f^a=fh,i^a=i^78,c^b=cf,d^b=dh,e^b=eh,g^b=gh,f^c=fh1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 78159);