Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#3289 ⋊ C2 |
| Sylow | C47 ⋊ #61108 |
2592 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 111 points:
(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)(49,59)(56,79)(57,81)(58,83)(60,61)(62,85)(67,87)(77,104)(78,102)(80,106)(82,89)(84,86)(88,96)(97,107)(103,111)(105,108);(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)(48,52)(49,58)(50,64)(51,68)(53,75)(54,72)(55,73)(56,78)(57,80)(59,83)(60,86)(61,84)(62,89)(63,90)(65,94)(66,95)(67,97)(69,100)(70,101)(71,74)(76,99)(77,103)(79,102)(81,106)(82,85)(87,107)(88,108)(91,110)(92,98)(93,109)(96,105)(104,111);(48,51,55,70)(49,57,59,81)(50,63,66,93)(52,68,73,101)(53,69,54,76)(56,77,79,104)(58,80,83,106)(60,67,61,87)(62,88,85,96)(64,90,95,109)(65,91,74,92)(71,98,94,110)(72,99,75,100)(78,103,102,111)(82,105,89,108)(84,107,86,97);(48,50)(49,56)(51,63)(52,71)(53,74)(54,65)(55,66)(57,77)(58,82)(59,79)(60,85)(61,62)(64,72)(67,96)(68,98)(69,92)(70,93)(73,94)(75,95)(76,91)(78,84)(80,105)(81,104)(83,89)(86,102)(87,88)(90,99)(97,111)(100,109)(101,110)(103,107)(106,108);(48,49)(50,62)(51,67)(52,58)(53,61)(54,60)(55,59)(56,65)(57,69)(63,77)(64,89)(66,85)(68,97)(70,87)(71,102)(72,86)(73,83)(74,79)(75,84)(76,81)(78,94)(80,100)(82,95)(88,92)(90,103)(91,96)(93,104)(98,108)(99,106)(101,107)(105,110)(109,111)Polycyclic presentation:
2^8,47|c^2=h,f^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,g^a=gh,d^b=df,f^b=fh,g^c=gh,f^d=fh,i^e=i^46650 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045843);