Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3300 ⋊ C2 |
| Sylow | C47 ⋊ #62101 |
1728 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 79 points:
(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)(48,51,52,60)(49,54,55,59)(50,58,57,63)(53,61,56,62);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(50,57)(53,56)(58,63)(61,62);(64,67,69,75)(65,71,72,79)(66,73,68,77)(70,78,76,74);(48,50)(49,53)(51,58)(52,57)(54,61)(55,56)(59,62)(60,63)(64,66,69,68)(65,70,72,76)(67,73,75,77)(71,78,79,74);(48,49,52,55)(50,56,57,53)(51,59,60,54)(58,61,63,62)(64,65)(66,70)(67,74)(68,76)(69,72)(71,73)(75,78)(77,79)Polycyclic presentation:
2^8,47|a^2=f,b^2=h,c^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,d^b=df,g^c=gh,i^e=i^46866 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1065182);