Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C4 · Schur multiplier (H2) = C228 |
| direct product | C26×#106 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C28 | D4 |
| commutator | C4 | C27×C4 |
| Frattini, cosocle | C2×C4 | C28 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C28 ◁ C27×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
2304360 conjugacy classes of subgroups; only the 1581160 normal subgroups are shown.
This group has 2304360 conjugacy classes of subgroups — too many to draw. Only its 1581160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2048 |
896 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C26×#442, C27×#106 |
| maximal normal subgroup of | C26×#442, C27×#106 |
| maximal quotient of | C27×#106 |
Past the SmallGroups library coverage — no SmallGroups id.