Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C217 |
| direct product | C22×C3×#2403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C3 | C24 |
| commutator, Frattini, cosocle | C23 | C26×C3 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C3 ◁ G | |
115796 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
456 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C22×D3×#2403, #72271170 |
| maximal subgroup of | C22×D3×#2403, C3×#72214549, #72271170 |
| maximal normal subgroup of | C22×D3×#2403, C3×#72214549, #72271170 |
| maximal quotient of | C3×#72214271 |
Past the SmallGroups library coverage — no SmallGroups id.