Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C221 |
| direct product | C22×C4×#3003 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | C22×D4 |
| commutator | C2×C4 | C26×C4 |
| Frattini, cosocle | C22×C4 | C27 |
| socle | C25 | C23×D4 |
| prime radical | C23×#3003 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ C25×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
935648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72310675 |
| maximal normal subgroup of | C2×#72310675 |
| automorphism group of | C16×D8, #12039, C16×Q16, … |
Past the SmallGroups library coverage — no SmallGroups id.