Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C42 |
| direct product | C2×#72261543 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C22×C42 |
| commutator | C22×C4 | C23×C42 |
| Frattini, cosocle | C22×C42 | C25 |
| socle | C24 | C22×#95 |
| prime radical | C27 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C42 ▷ C22 ▷ C1 | |
125968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72303335 |
| maximal normal subgroup of | #72303335 |
Past the SmallGroups library coverage — no SmallGroups id.