Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C215 |
| direct product | C22×C3×#3003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C3 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C3 ◁ C25×C3×C4 ◁ G | |
69980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
384 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C22×D3×#3003, #72255229, #72271534 |
| maximal subgroup of | C22×D3×#3003, C3×#72214076, #72255229, … |
| maximal normal subgroup of | C22×D3×#3003, C3×#72214076, #72255229, … |
Past the SmallGroups library coverage — no SmallGroups id.