Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3162 ⋊ C2 |
| Sylow | C47 ⋊ #60685 |
1878 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)(56,60,62,61)(57,65,66,76)(58,69,68,70)(59,73,75,74)(63,79,78,85)(64,71,81,87)(67,83,72,84)(77,82,80,86);(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)(48,50,51,54)(49,53,52,55)(58,68)(63,78)(67,72)(69,70)(77,80)(79,85)(82,86)(83,84);(56,59,61,74,62,75,60,73)(57,64,65,71,66,81,76,87)(58,67,70,84,68,72,69,83)(63,77,79,82,78,80,85,86);(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)(49,52)(53,55)(56,58)(57,63)(59,72)(60,69)(61,70)(62,68)(64,80)(65,79)(66,78)(67,75)(71,86)(73,84)(74,83)(76,85)(77,81)(82,87);(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)(50,53)(51,52)(54,55)(56,57)(58,63)(59,71)(60,65)(61,76)(62,66)(64,74)(67,82)(68,78)(69,79)(70,85)(72,86)(73,81)(75,87)(77,84)(80,83)Polycyclic presentation:
2^8,47|c^2=g,d^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^a=i^46,c^b=ch,d^b=dh,i^b=i^46,i^d=i^46800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1039470);