Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #9929 |
610 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 610 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) = 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)(85,90)(86,92)(88,94)(89,95)(91,98)(93,99)(96,97)(100,103,105,104)(101,107,108,112)(102,110,111,113)(106,114,115,109);(84,86,88,93)(85,89,91,96)(87,92,94,99)(90,97,98,95)(100,102,105,111)(101,106,108,115)(103,110,104,113)(107,114,112,109);(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)(84,85)(86,89)(87,90)(88,91)(92,95)(93,96)(94,98)(97,99)(100,101,105,108)(102,109,111,114)(103,107,104,112)(106,113,115,110)Polycyclic presentation:
2^8,79|a^2=g,b^2=gh,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,i^a=i^78,c^b=cf,d^b=dg,d^c=dh,i^c=i^781522 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 69870);