Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #9772 |
478 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 151 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)(88,91,93,104,94,105,92,103)(89,96,106,116,97,112,98,102)(90,99,107,117,100,114,101,115)(95,108,110,118,111,119,109,113);(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)(80,81,85,87,83,86,82,84)(88,90,92,101,94,100,93,107)(89,95,98,109,97,111,106,110)(91,99,103,115,105,114,104,117)(96,108,102,113,112,119,116,118);(81,84)(82,85)(86,87)(88,89,93,98,94,97,92,106)(90,95,101,110,100,111,107,109)(91,102,104,112,105,116,103,96)(99,113,115,108,114,118,117,119)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfg,c^2=eh,d^2=gh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fh,i^b=i^781768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 69030);