Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1376 ⋊ C2 |
| Sylow | C79 ⋊ #13534 |
330 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 101 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)(81,83)(84,87)(85,94)(86,92)(88,102)(89,103)(90,106)(91,101)(93,108)(95,111)(96,110)(97,109)(98,113)(99,100)(104,107)(105,115)(112,114);(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)(80,81)(82,83)(84,86,99,102,91,103,90,107)(85,93,97,115,98,111,114,110)(87,92,100,88,101,89,106,104)(94,108,109,105,113,95,112,96);(84,85,92,96,99,114,88,95,91,98,89,105,90,97,104,108)(86,94,101,111,107,109,100,110,103,113,87,93,102,112,106,115)Polycyclic presentation:
2^8,79|a^2=dg,b^2=degh,d^2=g,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,c^b=cf,d^b=dg,e^b=eg,g^b=gh,i^b=i^78,d^c=dg,e^c=eg,g^c=gh,i^c=i^782224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89672);