Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C32×D21 |
| Fitting, socle | C22×C33×C7 ⋊ C2 |
| derived | C3×C7 ⋊ C23×C32 |
| Hall | C33×C7 ⋊ C23 |
| Sylow | C33 ⋊ C22×D7 |
| Sylow | C7 ⋊ C22×C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C7 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C22×C32 | |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3⋊D3×D21, C22×C32×D3×D7 |
| maximal normal subgroup of | C22×C3⋊D3×D21, C22×C32×D3×D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 884);