Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3312 ⋊ C2 |
| Sylow | C47 ⋊ #61655 |
2032 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)(49,53)(52,54)(56,60,62,61)(57,66,65,74)(58,69,68,73)(59,71,72,75)(63,77,79,78)(64,81,80,70)(67,84,83,85)(76,82,86,87);(50,55)(52,54)(57,65)(58,68)(64,80)(66,74)(67,83)(69,73)(70,81)(84,85);(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)(56,59)(57,64)(58,67)(60,71)(61,75)(62,72)(63,76)(65,80)(66,81)(68,83)(69,84)(70,74)(73,85)(77,82)(78,87)(79,86);(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)(49,52)(51,55)(53,54)(56,58,62,68)(57,63,65,79)(59,67,72,83)(60,73,61,69)(64,76,80,86)(66,78,74,77)(70,82,81,87)(71,85,75,84);(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)(50,54)(51,53)(52,55)(56,57)(58,63)(59,70)(60,66)(61,74)(62,65)(64,71)(67,82)(68,79)(69,77)(72,81)(73,78)(75,80)(76,85)(83,87)(84,86)Polycyclic presentation:
2^8,47|b^2=h,e^2=h,g^2=h,b^a=bf,c^a=cg,d^a=dh,e^a=ef,g^a=gh,i^a=i^46,d^b=dfh,e^b=eh,i^b=i^46,g^c=gh,i^c=i^46,i^e=i^46713 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1056172);