Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C2×#72234135 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C23×#120 |
| commutator, Frattini, cosocle | C24 | C27 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25×D4 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
677882 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
290 conjugacy classes. The character table is too large to display.
| maximal quotient of | #72262696 |
Past the SmallGroups library coverage — no SmallGroups id.