Finite Group DatabasebetaFinite Group Databasebeta| order | 16384 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order ≥ 263 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C228 |
| abelian | C27×C128 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C64 | C28 |
| socle, prime radical | C28 | C64 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
2745121 conjugacy classes of subgroups.
16384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C27×C256, C26×C4×C128, C28×C128 |
| maximal normal subgroup of | C27×C256, C26×C4×C128, C28×C128 |
| maximal quotient of | C27×C256, C26×C4×C128, C28×C128 |
Past the SmallGroups library coverage — no SmallGroups id.