Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3377 ⋊ C2 |
| Sylow | C47 ⋊ #61473 |
1770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6016 |
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)(48,50,51,54)(49,53,52,55)(58,67)(62,76)(66,81)(68,83)(75,86)(77,84)(80,87)(82,85);(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)(53,55);(56,59,61,71)(57,63,65,78)(58,66,67,81)(60,73,74,70)(62,75,76,86)(64,79,72,69)(68,85,83,82)(77,87,84,80);(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)(50,53)(51,52)(54,55)(56,58)(57,62)(59,66)(60,68)(61,67)(63,75)(64,77)(65,76)(69,80)(70,82)(71,81)(72,84)(73,85)(74,83)(78,86)(79,87);(49,52)(53,55)(56,57,61,65)(58,62,67,76)(59,69,71,79)(60,72,74,64)(63,73,78,70)(66,80,81,87)(68,84,83,77)(75,85,86,82)Polycyclic presentation:
2^8,47|a^2=h,c^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,g^a=gh,d^b=df,e^b=eh,i^b=i^46,g^c=gh,i^d=i^46,i^e=i^46725 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1052000);