Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #12044 |
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 20224 |
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)(80,82,83,87,84,81,85,86)(89,95)(94,109)(96,111)(97,107)(98,115)(102,114)(110,113)(112,118);(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)(88,90,93,101)(89,94,95,109)(91,103,106,119)(92,108,104,100)(96,112,111,118)(97,113,107,110)(98,114,115,102)(99,116,117,105);(80,81,83,86,84,82,85,87)(88,89)(90,98)(91,102)(92,107)(93,95)(94,99)(96,105)(97,104)(100,118)(101,115)(103,113)(106,114)(108,112)(109,117)(110,119)(111,116)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=e,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=ch,d^a=df,f^a=fh,d^b=df,f^b=fh,i^b=i^782248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81312);