Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13532 |
312 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 312 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) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 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)(80,83)(81,89)(82,84)(85,99)(86,96)(87,97)(88,91)(90,109)(92,94)(93,108)(95,102)(98,101)(100,111)(103,104)(105,107)(106,110);(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)(80,82,95,99,86,98,87,104)(81,88,105,100,93,106,92,109)(83,101,102,103,96,84,97,85)(89,91,107,111,108,110,94,90);(80,81,84,90,95,105,85,91,86,93,101,111,87,92,103,110)(82,94,96,109,104,108,102,106,98,107,83,100,99,89,97,88)Polycyclic presentation:
2^8,79|a^2=d,b^2=deg,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,f^a=fh,c^b=cf,d^b=dg,e^b=eg,g^b=gh,i^b=i^78,d^c=dgh,e^c=egh,g^c=gh1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89661);