Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×#1088 |
| Fitting | C2×C7×H(3,𝔽3) ⋊ C4 |
| derived, Sylow | H(3,𝔽3) ⋊ C2×C4×C7 |
| Hall | C7×H(3,𝔽3) ⋊ C2×C4 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 549);