Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C210 |
| direct product | C2×#72241333 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #106654 |
| commutator | C23×C4 | C22×C42 |
| Frattini, cosocle | C22×H(5,𝔽2) | C24 |
| prime radical | C22×#3498 | C22 |
| LCS | G ▷ C23×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C22×H(5,𝔽2) ▷ C23 ▷ C2 ▷ C1 | |
At least 6549 conjugacy classes of subgroups; only the 1160 normal subgroups are shown.
152 conjugacy classes — view the full character table.
| maximal subgroup of | #72341652 |
| maximal normal subgroup of | #72341652 |
Past the SmallGroups library coverage — no SmallGroups id.