Finite Group DatabasebetaFinite Group Databasebeta| order | 18496 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#72213403 |
| Fitting, socle | C2×C172 ⋊ C2×C16 |
| derived, Sylow | C172 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72213403 |
| commutator, hypocenter | C172 | C22×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C172 | C2×C16 |
| prime radical | C2×D172 | C8 |
| cosocle | #72213191 | C23 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2 | |
308 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
88 conjugacy classes — view the full character table.
| maximal subgroup of | #72218906, D3×#72213403 |
| maximal normal subgroup of | #72218906 |
| maximal quotient of | #72218906, D3×#72213403 |
Past the SmallGroups library coverage — no SmallGroups id.