Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#72238013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #115690 |
| commutator | C23×D4 | C23×C4 |
| Frattini, cosocle | C22×H(5,𝔽2) | C24 |
| prime radical | C2×#6628896 | C2 |
| LCS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C22×H(5,𝔽2) ▷ C23 ▷ C2 ▷ C1 | |
At least 10900 conjugacy classes of subgroups; only the 832 normal subgroups are shown.
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72238017 |
| maximal normal subgroup of | C2×#72238017 |
Past the SmallGroups library coverage — no SmallGroups id.