Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C79×#3027 ⋊ C2 |
| Sylow | C79 ⋊ #13350 |
738 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 77 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:
(2,8)(5,18)(7,19)(9,22)(10,11)(12,25)(13,28)(14,30)(16,31)(20,21)(23,24)(26,27)(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)(2,7)(4,13)(5,14)(6,15)(8,21)(9,12)(10,19)(11,20)(16,29)(17,28)(18,30)(22,25)(23,26)(24,27)(31,32)(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)(3,12)(4,9)(5,8)(6,11)(7,13)(10,18)(14,25)(15,27)(16,22)(17,24)(19,32)(20,28)(21,29)(23,31)(26,30)Polycyclic presentation:
2^8,79|e^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,c^b=cf,g^b=gh,d^c=dg,e^c=eh,i^c=i^78,f^d=fh1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88550);