Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C28×C4 · Schur multiplier (H2) = C237 |
| direct product | C27×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C29 | C22 |
| commutator | C2 | C28×C4 |
| Frattini, cosocle | C22 | C29 |
| prime radical | C210 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C29 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
138297192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1024 |
1280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C27×#120, C26×#392, C2×#72286609, … |
| maximal normal subgroup of | C27×#120, C26×#392, C2×#72286609, … |
| maximal quotient of | C27×#102 |
Past the SmallGroups library coverage — no SmallGroups id.