Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1347 ⋊ C2 |
| Sylow | C79 ⋊ #12107 |
428 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 61 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) = 5056 |
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)(80,82)(81,84)(83,86)(85,87)(88,91,94,93)(89,96,98,108)(90,100,102,109)(92,103,107,106)(95,111,113,112)(97,104,115,118)(99,116,117,114)(101,105,110,119);(80,81)(82,84)(83,85)(86,87)(88,90)(89,95)(91,100)(92,105)(93,109)(94,102)(96,111)(97,114)(98,113)(99,104)(101,106)(103,110)(107,119)(108,112)(115,116)(117,118);(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)(84,87)(88,89,94,98)(90,99,102,117)(91,96,93,108)(92,104,107,118)(95,110,113,101)(97,103,115,106)(100,116,109,114)(105,111,119,112)Polycyclic presentation:
2^8,79|a^2=h,c^2=h,d^2=fh,f^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fh,i^a=i^78,d^b=df,e^b=eg,f^b=fh,d^c=dg,i^c=i^781165 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81694);