Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#95 |
| unambiguous semidirect product | (C7⋊#95)⋊C3 |
| Hall | C7⋊#95 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #95 |
| Sylow | C7 ⋊ C3×#95 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^2,3,2^3,7|a^2=d,b^2=e,b^a=bf,g^a=g^6,g^c=g^476 conjugacy classes — view the full character table.
| maximal subgroup of | #89265⋊C3, #89262⋊C3, #89332⋊C3, … |
| maximal normal subgroup of | #89265⋊C3, #89262⋊C3, #89332⋊C3, … |
| maximal quotient of | #89318⋊C3, #89319⋊C3, #89322⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 41);