Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3265 ⋊ C2 |
| Sylow | C47 ⋊ #61580 |
2120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 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)(56,59,61,60)(57,63,64,68)(58,67,66,69)(62,71,70,65);(50,55)(52,54);(56,58)(57,62)(59,67)(60,69)(61,66)(63,71)(64,70)(65,68);(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)(58,66)(62,70)(65,71)(67,69);(48,49)(50,54)(51,53)(52,55)(56,57,61,64)(58,65,66,71)(59,63,60,68)(62,69,70,67)Polycyclic presentation:
2^8,47|a^2=h,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,c^b=ch,d^b=df,i^b=i^46,g^c=gh,i^e=i^46716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1054559);