Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #13366 |
382 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 123 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)(81,83)(92,94,95,103)(93,99,98,113)(96,109,106,123)(97,112,107,105)(100,118,114,122)(101,119,111,116)(102,121,120,108)(104,117,115,110);(80,81)(82,83)(84,86,87,91)(85,88,89,90)(93,98)(99,113)(100,114)(101,111)(102,120)(108,121)(116,119)(118,122);(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)(84,85,87,89)(86,90,91,88)(92,93,95,98)(94,102,103,120)(96,108,106,121)(97,111,107,101)(99,115,113,104)(100,117,114,110)(105,122,112,118)(109,119,123,116)Polycyclic presentation:
2^8,79|a^2=d,b^2=dh,c^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^78,c^b=cf,e^c=eg,g^c=gh,i^c=i^783172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88648);