Finite Group DatabasebetaFinite Group Databasebeta| order | 37548 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×ΓL(1,𝔽8)⋊#10597010 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3×#10597010) |
| unambiguous semidirect product | (C7⋊#10597010)⋊C32 |
| unambiguous semidirect product | (C3×C7⋊#10597010)⋊C3 |
| Fitting, socle | C3×C7×C149 ⋊ C3×C4 |
| derived, Hall | C7×C149 ⋊ C32×C4 |
| Hall | C3×ΓL(1,𝔽8)×C149 ⋊ C4 |
| Hall | C7⋊#10597010 ⋊ C32 |
| Sylow | C149 ⋊ C3×ΓL(1,𝔽8)⋊C4 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #10597010 |
| Sylow | C7 ⋊ C32×#10597010 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3129 |
597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37548, 62);