Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C215 |
| direct product | C2×#72213729 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #14679 |
| commutator | C23×C4 | C24×C4 |
| Frattini, cosocle | C24×C4 | C25 |
| prime radical | C23×#3484 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C22 ▷ C1 | |
At least 7002 conjugacy classes of subgroups; only the 4800 normal subgroups are shown.
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214923 |
| maximal normal subgroup of | C2×#72214923 |
| maximal quotient of | C2×#72292882 |
Past the SmallGroups library coverage — no SmallGroups id.