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 ⋊ #131 |
| Sylow | C7 ⋊ #901 |
| Sylow | C3 ⋊ #6470 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|a^2=d,b^2=d,d^2=e,g^a=g^6,c^b=ce,f^b=f^290 conjugacy classes — view the full character table.
| maximal subgroup of | #13052485, #13052486, #13053359, … |
| maximal normal subgroup of | #13052485, #13052486, #13053359, … |
| maximal quotient of | #13052229, #13052234, #13052238, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 434);