Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #66632 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#66635 |
| Hall | C3×C7 ⋊ C2×Q16 |
| Sylow | C7 ⋊ C2×#216 |
| Sylow | C3 ⋊ C2×#1144 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | #13054608, #13054609, #13054612, … |
| maximal normal subgroup of | #13054608, #13054609, #13054612, … |
| maximal quotient of | #13056599, C2×#10620646, C2×#10620649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1008);