Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C22×#87284 |
| Fitting | C23×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C22×#3484 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C24×D3 |
| commutator, cosocle | C22×C3 | C27 |
| Frattini | C22 | C26×D3 |
| Fitting | C23×C3×H(5,𝔽2) | C2 |
| socle | C24×C3 | C25 |
| hypercenter | C23×H(5,𝔽2) | D3 |
| hypocenter | C3 | C22×#3484 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C23×H(5,𝔽2) | |
149300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72270018, #72271041, C22×D3×#3484, … |
| maximal normal subgroup of | #72270018, #72271041, C22×D3×#3484, … |
Past the SmallGroups library coverage — no SmallGroups id.