Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #66561 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#66566 |
| Hall | C3×C7 ⋊ C2×SD16 |
| Sylow | C7 ⋊ C2×#215 |
| Sylow | C3 ⋊ C2×#1132 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #13052410, #13052418, C4×#66566, … |
| maximal normal subgroup of | #13052410, #13052418, C4×#66566, … |
| maximal quotient of | #13052281, #13052287, #13052290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 458);