Finite Group DatabasebetaFinite Group Databasebeta| order | 16384 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2097152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C8 |
| abelian | C2×C8×C1024 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C512 | C23 |
| socle, prime radical | C23 | C4×C512 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C4×C512 ▷ C2×C256 ▷ C128 ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
553 conjugacy classes of subgroups.
16384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C8×C2048, C2×C16×C1024, C4×C8×C1024, … |
| maximal normal subgroup of | C2×C8×C2048, C2×C16×C1024, C4×C8×C1024, … |
| maximal quotient of | C2×C8×C2048, C2×C16×C1024, C4×C8×C1024, … |
Past the SmallGroups library coverage — no SmallGroups id.