Finite Group DatabasebetaFinite Group Databasebeta| order | 16384 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 51539607552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C163 |
| abelian | C162×C64 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C82×C32 | C23 |
| socle, prime radical | C23 | C82×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C82×C32 ▷ C42×C16 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
8825 conjugacy classes of subgroups.
16384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C162×C128, C16×C32×C64, C2×C162×C64 |
| maximal normal subgroup of | C162×C128, C16×C32×C64, C2×C162×C64 |
| maximal quotient of | C162×C128, C16×C32×C64, C2×C162×C64 |
Past the SmallGroups library coverage — no SmallGroups id.