Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1364 ⋊ C2 |
| Sylow | C79 ⋊ #11939 |
306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 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:
(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)(88,91,94,107)(89,96,99,115)(90,101,104,105)(92,93,106,109)(95,110,112,113)(97,114,108,98)(100,111,117,116)(102,118,119,103);(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)(80,81,83,85)(82,87,86,84)(88,90,94,104)(89,95,99,112)(91,101,107,105)(92,103,106,118)(93,102,109,119)(96,110,115,113)(97,116,108,111)(98,117,114,100);(81,84)(82,86)(85,87)(88,89,93,98,91,96,106,97,94,99,109,114,107,115,92,108)(90,100,103,112,105,116,119,110,104,117,118,95,101,111,102,113)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=h,d^2=gh,e^2=fgh,g^2=h,b^a=bd,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^c=i^781189 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 80852);