Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#3271 ⋊ C2 |
| Sylow | C47 ⋊ #61096 |
2686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 83 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)(52,55)(53,60)(54,64)(56,68)(57,67)(58,72)(59,74)(61,75)(62,66)(63,77)(65,80)(69,81)(70,79)(71,82)(73,78)(76,83);(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)(52,54,57,65)(53,59,62,73)(55,64,67,80)(56,70,69,63)(58,71,61,76)(60,74,66,78)(68,79,81,77)(72,82,75,83);(49,51)(55,67)(60,66)(64,80)(68,81)(72,75)(74,78)(77,79)(82,83);(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)(53,58)(54,63)(55,67)(56,69)(59,73)(60,75)(61,62)(64,79)(65,70)(66,72)(77,80)(82,83);(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)(52,53,57,62)(54,59,65,73)(55,66,67,60)(56,58,69,61)(63,76,70,71)(64,78,80,74)(68,75,81,72)(77,82,79,83)Polycyclic presentation:
2^8,47|a^2=h,d^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,i^a=i^46,d^b=df,e^b=eh,f^b=fh,i^b=i^46,e^c=eh,f^d=fh,i^d=i^46,i^e=i^46722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045723);