Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1383 ⋊ C2 |
| Sylow | C79 ⋊ #12563 |
570 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)(84,87,91,90)(85,93,96,107)(86,98,100,102)(88,103,89,104)(92,108,109,112)(94,105,95,106)(97,111,110,115)(99,113,101,114);(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)(84,86,89,101,90,102,103,113,91,100,88,99,87,98,104,114)(85,92,95,110,93,108,106,115,96,109,94,97,107,112,105,111);(84,85)(86,97,100,110)(87,93)(88,105)(89,106)(90,107)(91,96)(92,99,109,101)(94,104)(95,103)(98,111,102,115)(108,113,112,114)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=h,d^2=g,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,e^b=eh,i^c=i^781312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84471);