Finite Group DatabasebetaFinite Group Databasebeta| order | 3232 |
| automorphism | Aut(G) order 1292800 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D1616 |
| Fitting | C16×C101 ⋊ C2 |
| Sylow | C101 ⋊ D16 |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 1616 |
A minimal faithful permutation representation — 2 generators on 117 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,117)(19,116)(20,115)(21,114)(22,113)(23,112)(24,111)(25,110)(26,109)(27,108)(28,107)(29,106)(30,105)(31,104)(32,103)(33,102)(34,101)(35,100)(36,99)(37,98)(38,97)(39,96)(40,95)(41,94)(42,93)(43,92)(44,91)(45,90)(46,89)(47,88)(48,87)(49,86)(50,85)(51,84)(52,83)(53,82)(54,81)(55,80)(56,79)(57,78)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72)(64,71)(65,70)(66,69)(67,68)Polycyclic presentation:
2^5,101|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^100,c^b=cd,d^b=de,f^b=f^100811 conjugacy classes — view the full character table.
| maximal subgroup of | D4848, D8080, D11312, … |
| maximal quotient of | D4848, D8080, D11312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3232, 88);