Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×Q8⋊C16 ⋊ C2 |
| Sylow | C79 ⋊ #11622 |
320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 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:
(1,2)(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)(81,85)(84,87)(90,98)(94,104)(99,110)(100,111)(105,114)(106,115)(112,118)(116,119);(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)(80,81)(82,87)(83,85)(84,86)(88,90)(89,94)(91,99)(92,100)(93,98)(95,105)(96,106)(97,104)(101,112)(102,110)(103,111)(107,116)(108,114)(109,115)(113,118)(117,119);(81,84)(82,86)(85,87)(88,89,91,95,92,96,101,107,93,97,102,108,103,109,113,117)(90,94,99,105,100,106,112,116,98,104,110,114,111,115,118,119)Polycyclic presentation:
2^8,79|a^2=e,d^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,c^b=cfh,d^b=df,i^b=i^78,i^c=i^782260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79444);