Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C47×#3012 ⋊ C2 |
| Sylow | C47 ⋊ #60835 |
2040 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 87 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)(58,68)(59,72)(62,67)(64,71)(70,82)(73,84)(75,77)(78,79);(49,53)(52,54)(56,59)(57,64)(58,69)(60,72)(61,73)(62,76)(63,78)(65,71)(66,79)(67,80)(68,81)(70,83)(74,84)(75,85)(77,86)(82,87);(50,55)(52,54)(57,63)(58,68)(61,74)(62,75)(64,78)(65,66)(67,77)(69,81)(71,79)(73,84)(76,85)(80,86);(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)(48,50,51,55)(49,52,53,54)(56,58)(57,62)(59,69)(60,68)(61,70)(63,77)(64,76)(65,67)(66,75)(71,80)(72,81)(73,83)(74,82)(78,86)(79,85)(84,87);(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)(50,54)(51,53)(52,55)(56,57,60,65)(58,67,68,62)(59,71,72,64)(61,63,74,66)(69,76,81,80)(70,75,82,77)(73,79,84,78)(83,86,87,85)Polycyclic presentation:
2^8,47|a^2=h,b^2=fh,g^2=h,b^a=bf,c^a=cg,d^a=df,g^a=gh,i^a=i^46,c^b=cf,e^b=eh,i^b=i^46,g^c=gh,e^d=eh785 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1041538);