Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C2×#11703805 |
| Fitting | C23×C3×#120 ⋊ C2 |
| Sylow | C3 ⋊ C2×#62817 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C25×D3 |
| commutator, cosocle | C22×C3 | C27 |
| Frattini | C22 | C26×D3 |
| Fitting | C23×C3×#120 | C2 |
| socle | C23×C3 | C26 |
| hypercenter | C23×#120 | D3 |
| hypocenter | C3 | C2×#62817 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C23×#120 | |
92740 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#62817, C2×#72231395, C2×#72231340, … |
| maximal normal subgroup of | C2×D3×#62817, C2×#72231395, C2×#72231340, … |
Past the SmallGroups library coverage — no SmallGroups id.