Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1336 ⋊ C2 |
| Sylow | C79 ⋊ #12068 |
204 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 73 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:
(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)(80,83,97,103,102,111,84,99,86,101,108,109,85,100,92,98)(81,87,94,104,90,96,95,110,82,93,88,107,91,106,89,105);(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)(81,86)(83,93)(84,89)(85,90)(87,101)(88,97)(91,102)(92,95)(94,108)(96,100)(98,110)(99,105)(103,107)(104,109)(106,111);(80,81,84,89,85,91,97,88,86,82,92,95,102,90,108,94)(83,96,99,104,100,87,103,105,101,106,98,107,111,93,109,110)Polycyclic presentation:
2^8,79|a^2=e,c^2=ef,d^2=f,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=cf,d^a=df,f^a=fh,d^b=dfh,e^b=eh,f^b=fh,d^c=dh,i^c=i^781294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81455);