Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#2912 ⋊ C2 |
| Sylow | C47 ⋊ #61293 |
1874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,59)(57,64)(58,66)(60,68)(61,69)(62,70)(63,71)(65,67);(50,55)(53,54)(59,69)(64,67)(66,68)(70,71);(48,51,52,49)(50,54,55,53)(57,63)(58,60)(62,65)(64,71)(66,68)(67,70);(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)(48,50)(49,53)(51,54)(52,55)(56,58,61,60)(57,62,65,63)(59,68,69,66)(64,71,67,70);(48,49,52,51)(50,54,55,53)(56,57,61,65)(58,62,60,63)(59,67,69,64)(66,71,68,70)Polycyclic presentation:
2^8,47|a^2=fh,b^2=h,c^2=f,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,c^b=ch,d^b=df,e^b=eh,i^b=i^46,g^c=gh,e^d=eh1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1049090);