Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3360 ⋊ C2 |
| Sylow | C47 ⋊ #61331 |
1764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 87 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)(56,60,61,62)(57,65,66,75)(58,70,69,74)(59,72,73,76)(63,78,67,79)(64,80,81,71)(68,85,84,86)(77,87,82,83);(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)(48,50,51,55)(49,53,52,54)(58,69)(63,67)(68,84)(70,74)(77,82)(78,79)(83,87)(85,86);(56,59)(57,64)(58,68)(60,72)(61,73)(62,76)(63,77)(65,80)(66,81)(67,82)(69,84)(70,85)(71,75)(74,86)(78,87)(79,83);(48,49,51,52)(50,54,55,53)(56,58,61,69)(57,63,66,67)(59,68,73,84)(60,74,62,70)(64,77,81,82)(65,79,75,78)(71,87,80,83)(72,86,76,85);(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)(49,52)(53,54)(56,57)(58,67)(59,71)(60,65)(61,66)(62,75)(63,69)(64,72)(68,83)(70,79)(73,80)(74,78)(76,81)(77,85)(82,86)(84,87)Polycyclic presentation:
2^8,47|b^2=f,d^2=fh,e^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^a=i^46,d^b=df,e^b=eh,g^c=gh,i^d=i^46,i^e=i^46863 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1049628);