Finite Group DatabasebetaFinite Group Databasebeta| order | 12288 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order ≥ 263 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C228 |
| abelian | C27×C3×C32 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C28×C3 |
| socle, prime radical | C28×C3 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3938294 conjugacy classes of subgroups.
12288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C27×C3×C64, C28×C3×C32, C26×C3×C4×C32 |
| maximal normal subgroup of | C27×C3×C64, C28×C3×C32, C26×C3×C4×C32 |
| maximal quotient of | C27×C3×C64, C28×C3×C32, C26×C3×C4×C32 |
Past the SmallGroups library coverage — no SmallGroups id.