Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C7×C8 ⋊ C2 |
| Hall | C3×C7 ⋊ C22⋊C8 |
| Sylow | C7 ⋊ (C2×D3)⋊C8 |
| Sylow | C3 ⋊ (C2×D7)⋊C8 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=c,c^2=e,b^a=bd,f^a=f^2,g^a=g^6180 conjugacy classes — view the full character table.
| maximal subgroup of | #13052952, #13052953, #13052962, … |
| maximal normal subgroup of | #13052952, #13052953, #13052962, … |
| maximal quotient of | #13051366, #13051367, #13051371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 241);