Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C7×C8 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×M16 |
| Sylow | C7 ⋊ D3×M16 |
| Sylow | C3 ⋊ D7×M16 |
136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^5,3,7|c^2=d,d^2=e,c^a=ce,g^a=g^6,c^b=ce,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10620808, #13059177, #13059179, … |
| maximal normal subgroup of | C2×#10620808, #13059177, #13059179, … |
| maximal quotient of | #13052946, #13052950, #13052954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 390);