Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C7 ⋊ #102 |
| Sylow | C7 ⋊ #832 |
| Sylow | C3 ⋊ #6395 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=cd,c^2=e,b^a=bc,c^a=ce,g^a=g^6,f^b=f^296 conjugacy classes — view the full character table.
| maximal subgroup of | #13052256, #13052257, #13052258, … |
| maximal normal subgroup of | #13052256, #13052257, #13052258, … |
| maximal quotient of | #13050863, #13050880, #13050886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 82);