Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13169 |
286 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(84,87,98,108,89,101,105,115,90,102,86,97,104,114,88,100)(85,92,103,113,95,110,91,106,96,111,107,112,94,109,93,99);(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)(81,83)(84,86,89,88,90,98,104,105)(85,91,94,103,96,93,95,107)(87,97,101,100,102,108,114,115)(92,106,109,113,111,99,110,112);(80,81)(82,83)(84,85,89,94,90,96,104,95)(86,91,88,103,98,93,105,107)(87,99,101,112,102,106,114,113)(92,108,109,115,111,97,110,100)Polycyclic presentation:
2^8,79|a^2=f,b^2=f,c^2=eg,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^b=i^78,i^c=i^781792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 87617);