Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #66562 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#66562 |
| Hall | C3×C7 ⋊ C2×D8 |
| Sylow | C7 ⋊ C2×D24 |
| Sylow | C3 ⋊ C2×#1141 |
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#66562, #13052399, #13052403, … |
| maximal normal subgroup of | C4×#66562, #13052399, #13052403, … |
| maximal quotient of | #13052277, #13052283, #13052327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 446);