Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#20253752 |
| Fitting | C2×C47×#488 ⋊ C2 |
| Sylow | C47 ⋊ C2×#3137 |
2070 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 73 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)(60,67)(64,72)(66,73)(68,71);(51,55)(54,57)(58,61,62,65,63,69,70,59)(60,66,68,72,67,73,71,64);(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)(50,52,53,56)(51,54,55,57)(58,60,62,68,63,67,70,71)(59,64,61,66,65,72,69,73);(50,51)(52,54)(53,55)(56,57)(58,59,63,65)(60,66,67,73)(61,62,69,70)(64,71,72,68);(48,49)1076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038815);