Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#93266 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | #102 |
| commutator | C8 | C2×C82 |
| Frattini, cosocle | C42×C8 | C23 |
| socle | C23 | #1279 |
| prime radical | C24 | #339 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C22×C4×C8 ◁ C2×C42×C8 ◁ G | |
| LECS | G ▷ C42×C8 ▷ C22×C4 ▷ C2 ▷ C1 | |
1365 conjugacy classes of subgroups.
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72223649, C2×C8×#1336, C2×#72223664 |
| maximal normal subgroup of | C2×#72223649, C2×C8×#1336, C2×#72223664 |
Past the SmallGroups library coverage — no SmallGroups id.