Finite Group DatabasebetaFinite Group Databasebeta| order | 9216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3×#72215851 |
| Fitting | C2×C3×#347042 ⋊ C3 |
| Sylow | C2×#347042 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #72215851 |
| commutator, cosocle | C22×#120 | C23×C32 |
| Frattini | C25 | C23×C3×A4 |
| Fitting | C2×C3×#347042 | C3 |
| socle | C23×C3 | AΣL(1,𝔽64) |
| hypocenter | C26 | C2×C32×D4 |
| LCS | G ▷ C22×#120 ▷ C26 | |
| UCS | C1 ◁ C2×C3 | |
At least 9470 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has at least 9470 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#72215854 |
Past the SmallGroups library coverage — no SmallGroups id.