Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C79×#1361 ⋊ C2 |
| Sylow | C79 ⋊ #11963 |
396 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 396 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) = 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)(81,84)(85,87)(88,91,94,108)(89,96,99,100)(90,102,105,106)(92,93,107,110)(95,111,113,117)(97,98,109,115)(101,114,116,112)(103,118,119,104);(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)(81,84)(82,86)(88,90)(89,95)(91,102)(92,104)(93,103)(94,105)(96,111)(97,114)(98,116)(99,113)(100,117)(101,115)(106,108)(107,118)(109,112)(110,119);(80,81,82,85,83,84,86,87)(88,89,93,98,91,100,107,97,94,99,110,115,108,96,92,109)(90,101,104,113,106,114,119,117,105,116,118,95,102,112,103,111)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=gh,e^2=fgh,g^2=h,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,g^b=gh,i^c=i^781183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 80962);