Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C2×#10974249 |
| Fitting | C23×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C2×#35346 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C24×D3 |
| commutator, cosocle | C23×C3 | C26 |
| Frattini | C23 | C25×D3 |
| Fitting | C23×C3×H(5,𝔽2) | C2 |
| socle | C24×C3 | C25 |
| hypercenter | C23×H(5,𝔽2) | D3 |
| hypocenter | C3 | C2×#35346 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ C23×H(5,𝔽2) | |
67300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72231591, C2×#72230753, C2×D3×#35346 |
| maximal normal subgroup of | C2×#72231591, C2×#72230753, C2×D3×#35346 |
Past the SmallGroups library coverage — no SmallGroups id.