Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1511 ⋊ C2 |
| Sylow | C79 ⋊ #9982 |
722 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 79 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)(88,91,94,107)(89,96,99,114)(90,101,103,117)(92,106,93,108)(95,109,110,119)(97,113,98,115)(100,112,111,116)(102,105,104,118);(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)(88,90)(89,95)(91,105)(92,104)(93,102)(94,103)(96,112)(97,111)(98,100)(99,110)(101,106)(107,118)(108,117)(109,113)(114,116)(115,119);(80,81)(82,84)(83,85)(86,87)(88,89,94,99)(90,100,103,111)(91,96,107,114)(92,98,93,97)(95,104,110,102)(101,116,117,112)(105,119,118,109)(106,115,108,113)Polycyclic presentation:
2^8,79|a^2=g,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fgh,c^b=cf,d^b=dg,e^b=eg,f^b=fg,i^b=i^78,d^c=dh,f^c=fg,i^c=i^781042 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 70213);