Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×Q8×A4 |
| Fitting, Hall | C22×C7×Q8 ⋊ C3 |
| Sylow | C22×Q8 ⋊ C3×C7 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#5416, C7×#5417, #13057184, … |
| maximal normal subgroup of | C7×#5416, C7×#5417, #13057184, … |
| maximal quotient of | C7×A4×C4⋊C4, C7×#557⋊C3, C7×Q8×SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1188);