Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#939 |
| Fitting | C2×C3×C7×D4 ⋊ C2 |
| Hall | C3×C7 ⋊ #121 |
| Sylow | C3 ⋊ C7×#121 |
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3,4,5,6,7)(8,9,10)(12,14)(16,18);(15,16)(17,18);(9,10)(11,12)(13,14)(16,18)168 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#939, #13059918, #13059920, … |
| maximal normal subgroup of | D7×#939, #13059918, #13059920, … |
| maximal quotient of | C7×#4942, C7×#4957, C7×#4952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 918);