Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C7×D8 ⋊ C2 |
| Hall | C3×C7 ⋊ AGL(1,ℤ/8) |
| Sylow | C7 ⋊ #911 |
| Sylow | C3 ⋊ #6474 |
136 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 41 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|d^2=e,c^a=ce,f^a=f^2,g^a=g^6,c^b=cd,d^b=de,d^c=de81 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#911, D3×#6474, #13059278, … |
| maximal normal subgroup of | D7×#911, D3×#6474, #13059278, … |
| maximal quotient of | #13056396, #13056397, #13056398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 976);