Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×C7×C9 ⋊ C2×C3 |
| Hall | #4427 ⋊ D4 |
| Hall | C22⋊D7 ⋊ 3−1+2 |
| Sylow | C7 ⋊ D4×3−1+2 |
128 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2^2,3^2,2,3,7|d^3=f,b^a=be,g^a=g^6,d^c=df,g^c=g^291 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 155);