Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of Dic42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(C3⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | (C2×D84)⋊C3 |
| Fitting | C2×C3×C4×C7 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×C3×D12 |
232 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 659);