Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D7×D27 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D7×D27 |
| unambiguous semidirect product | (C7×D27)⋊C22 |
| unambiguous semidirect product | (D7×C27)⋊C22 |
| unambiguous semidirect product | D189⋊C22 |
| Fitting | C2×C7×C27 ⋊ C22 |
| derived, Hall | C7×C27 ⋊ C23 |
| Sylow | C27 ⋊ C22×D7 |
| Sylow | C7 ⋊ C22×D27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7×D27 |
| commutator, cosocle, hypocenter | C7×C27 | C23 |
| Frattini | C9 | C2×D3×D7 |
| Fitting | C2×C7×C27 | C22 |
| socle | C2×C3×C7 | C2×D9 |
| LCS | G ▷ C7×C27 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 378 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 89);