Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #1141⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#1141⋊C3 |
| unambiguous semidirect product | (C2×#1141)⋊C3 |
| Fitting | C2×C7×D4 ⋊ C2×C3 |
| Hall | C2×#1141 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×D8 |
| Sylow | C7 ⋊ C2×C3×D8 |
152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | #89521⋊C3, #89558⋊C3, #89559⋊C3, … |
| maximal normal subgroup of | #89521⋊C3, #89558⋊C3, #89559⋊C3, … |
| maximal quotient of | C2×#6381⋊C3, C2×#6383⋊C3, #89739⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 349);