Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C79 ⋊ #8799 |
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 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) = 127 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 127 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)(80,83,84,93,86,92,85,82)(81,88,89,95,91,94,90,87)(96,99,100,111,101,112,113,126)(97,103,104,116,105,110,117,125)(98,107,108,121,109,122,123,127)(102,114,106,118,115,124,119,120);(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)(80,82,84,83,86,93,85,92)(81,87,89,88,91,95,90,94)(96,98)(97,102,105,115)(99,107)(100,108)(101,109)(103,114,110,124)(104,106,117,119)(111,121)(112,122)(113,123)(116,118,125,120)(126,127);(80,81,85,89,86,91,84,90)(82,88,92,95,93,94,83,87)(96,97)(98,106,109,119)(99,110,112,103)(100,104)(101,105)(102,108,115,123)(107,120)(111,125,126,116)(113,117)(114,121)(118,122)(124,127)Polycyclic presentation:
2^8,79|a^2=f,b^2=eg,c^2=d,d^2=h,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=cg,f^b=fgh,i^b=i^78,f^c=fgh,i^c=i^781756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 63283);