Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ #135 |
| Sylow | C7 ⋊ #904 |
| Sylow | C3 ⋊ #6513 |
124 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 124 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.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=d,c^2=e,d^2=e,b^a=bd,g^a=g^6,d^b=de,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13052485, #13052486, #13053446, … |
| maximal normal subgroup of | #13052485, #13052486, #13053446, … |
| maximal quotient of | #13052278, #13052284, #13052328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 447);