Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3316 ⋊ C2 |
| Sylow | C47 ⋊ #61557 |
1820 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)(48,50,51,54)(49,53,52,55)(56,59,60,61)(57,64,62,68)(58,65,67,69)(63,70,66,71);(49,52)(53,55)(56,59,60,61)(57,64,62,68)(58,65,67,69)(63,70,66,71);(56,58,60,67)(57,63,62,66)(59,65,61,69)(64,70,68,71);(48,49)(50,53)(51,52)(54,55)(56,57,60,62)(58,66,67,63)(59,68,61,64)(65,70,69,71);(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)(57,62)(58,65)(59,61)(63,70)(66,71)(67,69)Polycyclic presentation:
2^8,47|b^2=h,c^2=h,d^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,d^a=dh,e^a=eh,g^a=gh,i^a=i^46,c^b=ch,d^b=df,e^b=eh,g^c=gh,i^e=i^46722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1054214);