Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#135×C47 ⋊ C2 |
| Sylow | C47 ⋊ #61290 |
1774 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 87 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,59,61,72)(57,64,66,70)(58,67,69,71)(60,73,74,85)(62,76,78,80)(63,79,65,81)(68,82,83,84)(75,86,77,87);(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)(50,55)(53,54)(59,72)(64,70)(67,71)(73,85)(76,80)(79,81)(82,84)(86,87);(48,51,52,49)(50,54,55,53)(57,63)(60,74)(62,75)(64,79)(65,66)(68,83)(70,81)(73,85)(76,86)(77,78)(80,87)(82,84);(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)(56,58,61,69)(57,62,66,78)(59,71,72,67)(60,68,74,83)(63,75,65,77)(64,80,70,76)(73,84,85,82)(79,87,81,86);(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)(48,49,52,51)(50,54,55,53)(56,57,61,66)(58,62,69,78)(59,70,72,64)(60,63,74,65)(67,80,71,76)(68,75,83,77)(73,81,85,79)(82,87,84,86)Polycyclic presentation:
2^8,47|a^2=fh,b^2=h,c^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,i^a=i^46,d^b=df,e^b=eh,i^b=i^46,g^c=gh,e^d=eh,i^d=i^461346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1049059);