Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C217 |
| direct product | C22×D3×#392 |
| Fitting | C22×C3×#392 ⋊ C2 |
| Sylow | C3 ⋊ C23×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C23×D3 |
| commutator, cosocle | C23×C3 | C26 |
| Frattini | C23 | C25×D3 |
| Fitting | C22×C3×#392 | C2 |
| socle | C25×C3 | C24 |
| hypercenter | C22×#392 | D3 |
| hypocenter | C3 | C23×#392 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C25 ◁ C22×#392 | |
139860 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#772778, D3×#234591, D3×#4928938, … |
| maximal normal subgroup of | D3×#772778, D3×#234591, D3×#4928938, … |
| maximal quotient of | D3×#4306523, D3×#6431795 |
| automorphism group of | #4454 |
Past the SmallGroups library coverage — no SmallGroups id.