Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13495 |
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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)(80,82,83,86)(81,85,84,87)(89,95)(90,99)(91,103)(92,104)(94,106)(96,97)(98,113)(100,116)(101,102)(105,118)(107,110)(108,119)(109,111)(112,114);(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)(85,87)(88,90)(89,94)(91,100)(92,99)(93,102)(95,111)(96,107)(97,109)(98,110)(101,104)(103,115)(105,116)(106,112)(108,114)(113,119)(117,118);(80,81)(82,85)(83,84)(86,87)(88,89,91,96,104,114,118,113,93,98,105,112,92,97,103,95)(90,94,100,107,101,108,117,119,102,110,116,106,99,109,115,111)Polycyclic presentation:
2^8,79|a^2=e,c^2=d,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,c^b=cf,f^b=fh,e^c=eg,f^c=fh,g^c=gh,i^c=i^782224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89441);