Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4 |
| direct product | C2×#72213409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #581603 |
| commutator | C22×C4 | C25×C4 |
| Frattini, cosocle | C23×C4 | C26 |
| prime radical | C2×#10575547 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
At least 7262 conjugacy classes of subgroups; only the 8200 normal subgroups are shown.
212 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213457, C2×#72216528, C2×#72216359 |
| maximal normal subgroup of | C2×#72213457, C2×#72216528, C2×#72216359 |
Past the SmallGroups library coverage — no SmallGroups id.