Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#3278 ⋊ C2 |
| Sylow | C47 ⋊ #61078 |
2694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 83 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)(53,62)(54,66)(60,70)(61,78)(64,71)(65,82)(68,81)(76,79);(52,56,58,69)(53,61,62,78)(54,65,66,82)(55,67,57,72)(59,74,75,83)(60,76,70,79)(63,80,73,77)(64,81,71,68);(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)(49,51)(52,55,58,57)(53,60,62,70)(54,64,66,71)(56,67,69,72)(59,73,75,63)(61,76,78,79)(65,81,82,68)(74,77,83,80);(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)(52,54)(53,59)(55,64)(56,68)(57,71)(58,66)(60,73)(61,77)(62,75)(63,70)(65,67)(69,81)(72,82)(74,79)(76,83)(78,80);(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)(50,51)(52,53,58,62)(54,63,66,73)(55,60,57,70)(56,61,69,78)(59,71,75,64)(65,80,82,77)(67,76,72,79)(68,83,81,74)Polycyclic presentation:
2^8,47|a^2=h,c^2=h,d^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,i^a=i^46,d^b=df,e^b=eh,f^b=fh,i^b=i^46,i^c=i^46,f^d=fh,i^e=i^46722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045448);