Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C22×#512862 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#2196 |
| commutator, Frattini, cosocle | #127 | C26 |
| LCS | G ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C24×C4 ◁ C23×#127 ◁ G | |
| LECS | G ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
95220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72213671 |
| maximal normal subgroup of | C22×#72213671 |
| maximal quotient of | #72338458 |
Past the SmallGroups library coverage — no SmallGroups id.