Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22 |
| direct product | C2×C7×ΓL(1,𝔽25) |
| Fitting | C2×C3×C7×C8 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×M16 |
| Sylow | C3 ⋊ C2×C7×M16 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | #13050911, C7×#4514, Dic7×ΓL(1,𝔽25), … |
| maximal normal subgroup of | #13050911, C7×#4514, Dic7×ΓL(1,𝔽25), … |
| maximal quotient of | C7×#4679, C7×#4685, C4×C7×ΓL(1,𝔽25), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 879);