Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1356 ⋊ C2 |
| Sylow | C79 ⋊ #11912 |
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 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)(81,87,90,103)(83,96)(84,94)(85,92)(86,91,88,104)(89,107,106,102)(93,97)(95,110)(98,101)(99,109)(100,111,105,108);(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)(81,86)(83,95)(84,99)(87,91)(88,90)(89,106)(93,101)(94,109)(96,110)(97,98)(102,107)(103,104);(80,81,83,89,84,86,98,100,85,90,97,106,99,88,95,105)(82,91,93,108,94,103,110,107,92,104,96,111,109,87,101,102)Polycyclic presentation:
2^8,79|a^2=e,c^2=g,d^2=g,e^2=f,f^2=h,b^a=bd,c^a=cf,d^a=df,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,i^b=i^78,d^c=dh,e^c=eh,i^c=i^78,e^d=eh814 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 80749);