Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1395 ⋊ C2 |
| Sylow | C79 ⋊ #12589 |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 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)(82,93)(87,102)(92,104)(94,96)(95,98)(101,109)(103,111)(108,110);(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)(80,82,85,96,86,93,83,94)(81,87,90,104,91,102,88,92)(84,98,99,101,100,95,97,109)(89,103,106,110,107,111,105,108);(80,81,84,89)(82,92,95,108)(83,90,97,106)(85,88,99,105)(86,91,100,107)(87,101,103,94)(93,104,98,110)(96,102,109,111)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,d^2=h,f^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,c^b=ch,e^b=egh,i^c=i^78,e^d=eh1060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84561);