Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13462 |
476 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,4,5,3)(2,6,7,8)(9,11)(10,14)(12,18)(13,19)(15,17)(16,22)(20,21)(23,24)(25,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27);(1,3,5,4)(2,6,7,8)(12,20)(15,23);(1,2,5,7)(3,8,4,6)(9,10,13,16)(11,17,19,24)(12,15,20,23)(14,21,22,18)(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)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)Polycyclic presentation:
2^8,79|a^2=dh,b^2=d,c^2=d,b^a=bd,c^a=ce,f^a=fgh,i^a=i^78,c^b=cf,e^b=eg,g^c=gh,f^e=fh1279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89243);