Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1849 ⋊ C2 |
| Sylow | C79 ⋊ #13487 |
338 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 99 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)(84,86,87,95,90,97,88,96)(85,92,89,94,93,99,91,98);(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)(85,91)(86,92)(87,88)(89,93)(94,96)(95,98)(97,99);(80,81,82,83)(84,85,88,91,90,93,87,89)(86,94,95,99,97,98,96,92)Polycyclic presentation:
2^8,79|a^2=e,c^2=d,d^2=h,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,f^a=fh,c^b=cf,d^b=dh,e^b=eh,f^b=fg,g^b=gh,i^b=i^78,e^c=eh,f^c=fgh,g^c=gh1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89394);