Finite Group DatabasebetaFinite Group Databasebeta| order | 1632 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#859 |
| derived | SL(2,𝔽3) ⋊ C4×C17 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23,29,24,25,28,27,26);(23,26,29)(24,27,28)272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1632, 252);