Finite Group DatabasebetaFinite Group Databasebeta| order | 16384 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8388608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C16 |
| abelian | C2×C16×C512 |
| multiplicative | (ℤ/34816)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C256 | C23 |
| socle, prime radical | C23 | C8×C256 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C8×C256 ▷ C4×C128 ▷ C2×C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
937 conjugacy classes of subgroups.
16384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C16×C1024, C2×C32×C512, C4×C16×C512, … |
| maximal normal subgroup of | C2×C16×C1024, C2×C32×C512, C4×C16×C512, … |
| maximal quotient of | C2×C16×C1024, C2×C32×C512, C4×C16×C512, … |
Past the SmallGroups library coverage — no SmallGroups id.