Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ C22⋊Q8 |
| Sylow | C7 ⋊ #878 |
| Sylow | C3 ⋊ #6459 |
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=d,c^2=e,c^a=cde,g^a=g^6,c^b=ce,f^b=f^278 conjugacy classes — view the full character table.
| maximal subgroup of | #13057750, #13057753, #13057755, … |
| maximal normal subgroup of | #13057750, #13057753, #13057755, … |
| maximal quotient of | #13053135, #13053136, #13053137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 574);