Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1858 ⋊ C2 |
| Sylow | C79 ⋊ #12975 |
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 points:
(2,9)(3,14)(5,21)(8,23)(10,28)(11,12)(13,29)(15,18)(17,27)(19,22)(24,31)(25,26)(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)(104,105)(106,107)(108,109)(110,111);(1,3,6,15,7,14,4,18)(2,8,10,24,12,25,17,13)(5,20,22,32,21,16,19,30)(9,26,28,29,11,23,27,31)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,2,6,10,7,12,4,17)(3,13,15,8,14,24,18,25)(5,9,22,28,21,11,19,27)(16,31,30,26,20,29,32,23)Polycyclic presentation:
2^8,79|a^2=f,b^2=f,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,c^b=ch,d^b=dh,e^b=egh,d^c=dg,e^c=eh,i^c=i^78,e^d=eh1288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86415);