Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C222 |
| direct product | C22×#6437510 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C23×D4 |
| commutator, Frattini, cosocle | C22×C4 | C27 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ C24×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Only the 48360 normal subgroups are shown; non-normal subgroups are omitted.
344 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72239586 |
| maximal normal subgroup of | C2×#72239586 |
| maximal quotient of | C2×#72237167, #72305173, C2×#72311718, … |
Past the SmallGroups library coverage — no SmallGroups id.