Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#72216449 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #134045 |
| commutator | C26 | C23×C4 |
| Frattini, cosocle | C2×#379 | C24 |
| prime radical | C2×#6499867 | C2 |
| LCS | G ▷ C26 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C26 ◁ C22×#2846 ◁ G | |
| LECS | G ▷ C2×#379 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
72924 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216466, C2×#72216698, C2×#72216682 |
| maximal normal subgroup of | C2×#72216466, C2×#72216698, C2×#72216682 |
Past the SmallGroups library coverage — no SmallGroups id.