Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C22×#87239 |
| Fitting | C25×C3×D4 ⋊ C2 |
| Sylow | C3 ⋊ C22×#3484 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C24×D3 |
| commutator, cosocle | C22×C3 | C27 |
| Frattini | C22 | C26×D3 |
| Fitting | C25×C3×D4 | C2 |
| socle | C24×C3 | C25 |
| hypercenter | C25×D4 | D3 |
| hypocenter | C3 | C22×#3484 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C25×D4 | |
149300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72270923, #72270938, #72270956, … |
| maximal normal subgroup of | #72270923, #72270938, #72270956, … |
Past the SmallGroups library coverage — no SmallGroups id.