Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3111 ⋊ C2 |
| Sylow | C47 ⋊ #62160 |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 95 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)(48,51,52,60)(49,54,55,59)(50,58,57,63)(53,61,56,62)(66,77)(71,86)(75,91)(76,78)(84,95)(85,92)(89,94)(90,93);(50,57)(53,56)(58,63)(61,62)(64,68,70,69)(65,73,74,82)(66,76,77,78)(67,80,81,83)(71,85,86,92)(72,87,88,79)(75,90,91,93)(84,94,95,89);(64,67)(65,72)(66,75)(68,80)(69,83)(70,81)(71,84)(73,87)(74,88)(76,90)(77,91)(78,93)(79,82)(85,94)(86,95)(89,92);(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)(51,58)(52,57)(54,61)(55,56)(59,62)(60,63)(64,66,70,77)(65,71,74,86)(67,75,81,91)(68,76,69,78)(72,84,88,95)(73,85,82,92)(79,89,87,94)(80,90,83,93);(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)(48,49,52,55)(50,56,57,53)(51,59,60,54)(58,61,63,62)(64,65)(66,71)(67,79)(68,73)(69,82)(70,74)(72,80)(75,89)(76,85)(77,86)(78,92)(81,87)(83,88)(84,90)(91,94)(93,95)Polycyclic presentation:
2^8,47|a^2=f,b^2=h,d^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,i^a=i^46,d^b=df,e^b=eh,i^b=i^46,g^c=gh785 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1066422);