Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C79×#1397 ⋊ C2 |
| Sylow | C79 ⋊ #13723 |
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 119 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)(81,85)(84,87)(88,90,91,101,104,114,108,99,94,102,105,116,110,111,96,100,95,103,106,117,118,119,112,115,109,113,107,98,93,97,92,89);(80,82,83,86)(81,84,85,87)(88,89,96,111,93,98,105,102,109,115,108,114,118,117,91,90,95,100,92,97,110,116,107,113,94,99,112,119,104,101,106,103);(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)(80,81)(82,84)(83,85)(86,87)(89,90)(91,92)(93,104)(94,109)(96,106)(97,101)(98,114)(99,113)(100,103)(102,115)(105,112)(107,108)(110,118)(111,117)(116,119)Polycyclic presentation:
2^8,79|b^2=eh,c^2=d,d^2=fg,e^2=f,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,g^a=gh,i^a=i^78,c^b=ch3166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90555);