Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219 |
| direct product | C2×D3×#3537 |
| Fitting | C2×C3×#3537 ⋊ C2 |
| Sylow | C3 ⋊ C22×#3537 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C25×D3 |
| commutator, cosocle | C22×C3 | C27 |
| Frattini | C22 | C26×D3 |
| Fitting | C2×C3×#3537 | C2 |
| socle | C23×C3 | C26 |
| hypercenter | C2×#3537 | D3 |
| hypocenter | C3 | C22×#3537 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C2×#3537 | |
84908 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#7918389, C2×D3×#12755, D3×#7837029, … |
| maximal normal subgroup of | D3×#7918389, C2×D3×#12755, D3×#7837029, … |
| maximal quotient of | C2×D3×#45355, C2×D3×#52004 |
Past the SmallGroups library coverage — no SmallGroups id.