Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ AGL(1,ℤ/8) |
| Sylow | C7 ⋊ #932 |
| Sylow | C3 ⋊ #6471 |
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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|b^2=d,d^2=e,b^a=bd,d^a=de,g^a=g^6,c^b=ce,f^b=f^275 conjugacy classes — view the full character table.
| maximal subgroup of | #13052493, #13052500, #13053455, … |
| maximal normal subgroup of | #13052493, #13052500, #13053455, … |
| maximal quotient of | #13052257, #13052260, #13052300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 456);