Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D7)⋊(C3⋊C8) |
| Hall | C3×C7 ⋊ C22⋊C8 |
| Sylow | C7 ⋊ #830 |
| 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,g^a=g^6,f^b=f^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #13052245, #13052246, #13052247, … |
| maximal normal subgroup of | #13052245, #13052246, #13052247, … |
| maximal quotient of | #13050862, #13050863, #13050868, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 72);