Finite Group DatabasebetaFinite Group Databasebeta| order | 1932 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×ΓL(1,𝔽8)⋊C4 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C4×C23) |
| unambiguous semidirect product | Dic7⋊(C3×C23) |
| unambiguous semidirect product | (C23×Dic7)⋊C3 |
| derived, Sylow | C7 ⋊ C3×C4×C23 |
| Hall | C23×Dic7 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C23 ⋊ C4 |
| Hall | C7×C23 ⋊ C3×C4 |
| Hall | Dic7 ⋊ C3×C23 |
| Hall | ΓL(1,𝔽8) ⋊ C4×C23 |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 644 |
A minimal faithful permutation representation — 2 generators on 34 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,29,28,26,27,30)(31,32,33,34);(24,25,28,29,27,30,26)322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1932, 2);