Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×#365×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13502 |
276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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)(81,89,90,102)(82,94)(83,87)(84,85)(88,104,93,105)(91,92,109,101)(96,97)(99,100)(103,110)(106,111,107,108);(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)(81,88)(83,98)(84,94)(85,96)(86,97)(87,103)(89,108)(90,93)(91,104)(92,107)(95,100)(99,110)(101,106)(102,111)(105,109);(80,81,87,102,84,101,83,91,86,90,99,89,85,92,100,109)(82,93,110,111,94,107,95,104,97,88,103,108,96,106,98,105)Polycyclic presentation:
2^8,79|a^2=eg,c^2=d,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,c^b=cf,e^b=eh,f^b=fh,i^b=i^78,e^c=eg,f^c=fh,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, 89483);