Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3363 ⋊ C2 |
| Sylow | C47 ⋊ #61846 |
1664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 79 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)(49,55)(53,56)(54,63)(61,62)(64,66,68,69)(65,70,72,73)(67,74,76,77)(71,75,78,79);(48,51,52,60)(49,54,55,63)(50,57,58,59)(53,61,56,62);(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)(64,67)(65,71)(66,74)(68,76)(69,77)(70,75)(72,78)(73,79);(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)(48,50,52,58)(49,53,55,56)(51,59,60,57)(54,62,63,61)(64,66,68,69)(65,70,72,73)(67,74,76,77)(71,75,78,79);(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)(50,56)(51,54)(52,55)(53,58)(57,62)(59,61)(60,63)(64,65,68,72)(66,73,69,70)(67,75,76,79)(71,77,78,74)Polycyclic presentation:
2^8,47|a^2=h,b^2=f,d^2=fh,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,i^a=i^46,d^b=dfh,i^b=i^46,g^c=gh,i^c=i^46,i^e=i^46857 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1059895);