Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C212 |
| direct product | C2×#72216447 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#12707 |
| commutator | #117 | C24×C4 |
| Frattini, cosocle | #535 | C25 |
| prime radical | C2×#10577314 | C2 |
| LCS | G ▷ #117 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C24×C4 ◁ C22×#3484 ◁ G | |
| LECS | G ▷ #535 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
At least 9475 conjugacy classes of subgroups; only the 1952 normal subgroups are shown.
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216489 |
| maximal normal subgroup of | C2×#72216489 |
Past the SmallGroups library coverage — no SmallGroups id.