Finite Group DatabasebetaFinite Group Databasebeta| order | 16384 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9663676416 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C64 |
| abelian | C22×C642 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C322 | C24 |
| socle, prime radical | C24 | C322 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C322 ▷ C162 ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
7217 conjugacy classes of subgroups.
16384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C64×C128, C2×C4×C642, C23×C642 |
| maximal normal subgroup of | C22×C64×C128, C2×C4×C642, C23×C642 |
| maximal quotient of | C22×C64×C128, C2×C4×C642, C23×C642 |
Past the SmallGroups library coverage — no SmallGroups id.