Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ C4×Dic6 |
| Sylow | C3 ⋊ #6450 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^5,3,7|a^2=d,b^2=de,c^2=e,g^a=g^6,c^b=ce,f^b=f^290 conjugacy classes — view the full character table.
| maximal subgroup of | #13052566, #13052568, #13052570, … |
| maximal normal subgroup of | #13052566, #13052568, #13052570, … |
| maximal quotient of | #13052229, #13052230, #13052240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 477);