Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×C4×#1891 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | #120 |
| commutator | C23 | C23×C42 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C23 | C2×#386 |
| prime radical | C22×#525 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
15525 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×#23882, C2×#72252569, C2×#72216090 |
| maximal normal subgroup of | C2×C4×#23882, C2×#72252569, C2×#72216090 |
Past the SmallGroups library coverage — no SmallGroups id.