Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3099 ⋊ C2 |
| Sylow | C47 ⋊ #60773 |
2118 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)(59,70)(63,77)(68,81)(71,83)(76,86)(78,84)(80,87)(82,85);(49,53)(52,54)(56,59)(57,63)(58,68)(60,71)(61,70)(62,76)(64,78)(65,77)(66,80)(67,81)(69,82)(72,84)(73,85)(74,83)(75,86)(79,87);(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)(52,54)(56,58,61,67)(57,62,65,75)(59,68,70,81)(60,73,74,69)(63,76,77,86)(64,79,72,66)(71,85,83,82)(78,87,84,80);(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)(49,52)(51,55)(53,54)(58,67)(62,75)(66,79)(68,81)(69,73)(76,86)(80,87)(82,85);(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)(56,57,61,65)(58,66,67,79)(59,63,70,77)(60,72,74,64)(62,73,75,69)(68,80,81,87)(71,84,83,78)(76,85,86,82)Polycyclic presentation:
2^8,47|a^2=h,c^2=h,g^2=h,b^a=bf,c^a=cg,d^a=df,g^a=gh,i^a=i^46,c^b=cfh,i^b=i^46,g^c=gh,i^c=i^46,e^d=eh782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1040717);