Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×#368×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13470 |
326 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 326 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) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(81,83)(85,93)(86,100)(87,99)(88,106)(89,91)(94,107)(95,96)(97,105)(98,113)(101,104)(102,108)(103,115)(109,110)(111,114);(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)(80,81)(82,83)(84,86,99,115,89,103,106,100,90,104,88,102,91,108,87,101)(85,92,105,113,96,111,95,109,97,112,93,110,107,114,94,98);(84,85,91,96,90,97,89,107)(86,98,108,113,104,109,103,110)(87,105,88,95,106,93,99,94)(92,102,111,100,112,115,114,101)Polycyclic presentation:
2^8,79|a^2=de,b^2=dg,d^2=gh,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fgh,g^a=gh,c^b=cf,d^c=dg,e^c=eg,f^c=fgh,g^c=gh,i^c=i^781756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89288);