Finite Group DatabasebetaFinite Group Databasebeta| order | 13872 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#72213364 |
| Fitting, socle, derived, Hall | C3×C172 ⋊ C22×C4 |
| Sylow | C172 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×#72213364 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C172 | C22×C4 |
| prime radical | D3×D172 | C2 |
| cosocle | C3×C17⋊D17 | C23 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 | |
344 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 344 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) = 102 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72213374 |
| maximal normal subgroup of | D3×#72213374 |
Past the SmallGroups library coverage — no SmallGroups id.