Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3385 ⋊ C2 |
| Sylow | C47 ⋊ #61384 |
1726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 6016 |
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)(56,60)(57,59)(58,66)(61,64)(62,68)(63,65)(67,70)(69,71);(48,51,52,49)(50,53,55,54)(56,59,61,68)(57,64,62,60)(58,65,67,71)(63,70,69,66);(56,58,61,67)(57,63,62,69)(59,65,68,71)(60,66,64,70);(48,50,52,55)(49,53,51,54)(56,57,61,62)(58,63,67,69)(59,60,68,64)(65,66,71,70);(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)(48,49,52,51)(50,54,55,53)(57,62)(58,63)(60,64)(65,70)(66,71)(67,69)Polycyclic presentation:
2^8,47|a^2=fh,b^2=f,c^2=h,d^2=f,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,i^a=i^46,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, 1050403);