Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#373683 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #2403 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C23×C4 | C25 |
| prime radical | C23×H(5,𝔽2) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
19749 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×#23882, C2×#72252512, C2×#72310607 |
| maximal normal subgroup of | C2×C4×#23882, C2×#72252512, C2×#72310607 |
Past the SmallGroups library coverage — no SmallGroups id.