Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C8 · Schur multiplier (H2) = C214 |
| direct product | C22×#483590 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | #442 |
| commutator | C8 | C25×C8 |
| Frattini, cosocle | C4×C8 | C26 |
| socle | C24 | C2×#442 |
| prime radical | C23×#509 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ C23×C42 ◁ C23×#322 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
25860 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#72216771 |
| maximal normal subgroup of | C22×#72216771 |
Past the SmallGroups library coverage — no SmallGroups id.