Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×H(3,𝔽3)×Dic7 |
| Hall | C7×H(3,𝔽3) ⋊ C2×C4 |
| Sylow | C7 ⋊ C2×C4×H(3,𝔽3) |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 350);