Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3113 ⋊ C2 |
| Sylow | C47 ⋊ #62168 |
1628 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)(65,72)(66,76)(71,86)(73,82)(75,91)(77,93)(78,87)(92,94);(50,57)(53,56)(58,63)(61,62)(66,76)(70,74)(75,91)(77,93)(84,88)(85,89)(90,95)(92,94);(64,67,68,79)(65,71,72,86)(66,75,76,91)(69,83,81,80)(70,84,74,88)(73,87,82,78)(77,94,93,92)(85,90,89,95);(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)(65,70)(67,75)(68,76)(69,77)(71,84)(72,74)(73,85)(78,95)(79,91)(80,92)(81,93)(82,89)(83,94)(86,88)(87,90);(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)(66,74)(67,78)(68,72)(69,82)(70,76)(71,80)(73,81)(75,90)(77,85)(79,87)(83,86)(84,94)(88,92)(89,93)(91,95)Polycyclic presentation:
2^8,47|a^2=fh,c^2=h,e^2=fh,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, 1066604);