Finite Group DatabasebetaFinite Group Databasebeta| order | 9216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C28 |
| direct product | C2×#72231618 |
| Fitting | C23×C3×H(5,𝔽2) ⋊ C2×D3 |
| derived | C3×C22⋊#997 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72231611 |
| commutator, cosocle, hypocenter | C3×C22⋊#997 | C23 |
| Frattini | C23 | C2×D3×#1020 |
| Fitting | C23×C3×H(5,𝔽2) | C2×D3 |
| socle | C24×C3 | C2×#1020 |
| LCS | G ▷ C3×C22⋊#997 | |
| UCS | C1 ◁ C22 | |
At least 8302 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has at least 8302 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
138 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.