Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | C22×#15689476 |
| Sylow | C47 ⋊ C22×#488 |
2310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 75 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)(53,57)(56,59)(60,63,64,72,65,73,71,62)(61,67,68,66,69,70,74,75);(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)(52,54,55,58)(53,56,57,59)(60,62,71,73,65,72,64,63)(61,66,74,67,69,75,68,70);(52,53)(54,56)(55,57)(58,59)(60,61)(62,70)(63,66)(64,74)(65,69)(67,72)(68,71)(73,75);(50,51);(48,49)1376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038761);