Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #11260 |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 points:
(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)(84,87)(85,92,93,107)(86,97)(88,101)(89,104)(90,102)(91,105,96,110)(94,100,95,109)(98,112)(99,114)(103,113)(106,115,108,111);(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)(84,86,88,98,90,99,89,103)(85,91,94,106,93,96,95,108)(87,97,101,112,102,114,104,113)(92,105,100,115,107,110,109,111);(84,85,89,95,90,93,88,94)(86,96,98,108,99,91,103,106)(87,100,101,107,102,109,104,92)(97,111,113,110,114,115,112,105)Polycyclic presentation:
2^8,79|a^2=g,b^2=e,c^2=d,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,g^b=gh,g^c=gh,i^c=i^781768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 77776);