Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D32×C7 |
| unambiguous semidirect product | (C3×D3)⋊(C22×C3×C7) |
| Fitting, socle | C2×C33×C7 ⋊ C22 |
| derived | C32 ⋊ C23×C3×C7 |
| Hall | C33×C7 ⋊ C23 |
| Sylow | C33 ⋊ C23×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D32 |
| commutator, cosocle, hypocenter | C32 | C23×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C7 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C3×C7 | |
324 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 869);