Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Hall | C7×H(3,𝔽3) ⋊ D4 |
| Sylow | H(3,𝔽3) ⋊ C22⋊D7 |
| Sylow | C7 ⋊ C4⋊((C3⋊D3)⋊C3) |
124 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2^2,3,2,3^2,7|a^2=d,b^a=bd,g^a=g^6,e^b=e^2,f^b=f^2,e^c=ef91 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 240);