Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of (C3⋊D3)⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×(C3⋊D3)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C4×C3⋊D3)⋊ΓL(1,𝔽8) |
| Fitting | C32×C4×C7 ⋊ C2×C3 |
| derived | C32×C7 ⋊ C2×C3×C4 |
| Hall | C7⋊H(3,𝔽3) ⋊ C2×C4 |
| Sylow | C7 ⋊ C4×(C3⋊D3)⋊C3 |
124 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
88 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 190);