Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3317 ⋊ C2 |
| Sylow | C47 ⋊ #61488 |
1788 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 87 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)(48,50,51,54)(49,53,52,55)(58,70)(63,67)(68,85)(69,74)(77,82)(78,79)(83,87)(84,86);(49,52)(53,55)(56,60,61,62)(57,65,66,75)(58,69,70,74)(59,72,73,76)(63,78,67,79)(64,80,81,71)(68,84,85,86)(77,87,82,83);(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)(56,59,61,73)(57,64,66,81)(58,68,70,85)(60,72,62,76)(63,77,67,82)(65,80,75,71)(69,84,74,86)(78,87,79,83);(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)(50,53)(51,52)(54,55)(56,58)(57,63)(59,68)(60,74)(61,70)(62,69)(64,77)(65,79)(66,67)(71,87)(72,86)(73,85)(75,78)(76,84)(80,83)(81,82);(49,52)(53,55)(56,57)(58,67)(59,71)(60,65)(61,66)(62,75)(63,70)(64,72)(68,83)(69,79)(73,80)(74,78)(76,81)(77,84)(82,86)(85,87)Polycyclic presentation:
2^8,47|c^2=h,d^2=h,e^2=fh,g^2=h,b^a=bf,c^a=cg,g^a=gh,d^b=df,e^b=eh,i^b=i^46,g^c=gh,i^c=i^46,i^e=i^46725 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1052307);