Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | Q8×C22⋊ΓL(1,𝔽8) |
| Fitting, Hall | C22×C7×Q8 ⋊ C3 |
| Sylow | C22×Q8 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ Q8×A4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #1143⋊A4, #1144⋊A4, SD16×C22⋊ΓL(1,𝔽8), … |
| maximal normal subgroup of | #1143⋊A4, #1144⋊A4, SD16×C22⋊ΓL(1,𝔽8), … |
| maximal quotient of | C4⋊C4×C22⋊ΓL(1,𝔽8), #557⋊ΓL(1,𝔽8), Q8×C7⋊SL(2,𝔽3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1195);