Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #92835 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#92837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #1270 |
| commutator | C4×C8 | C22×C8 |
| Frattini, cosocle | #1744 | C23 |
| prime radical | C2×#3169 | C4 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ C2×#1744 ◁ G | |
| LECS | G ▷ #1744 ▷ C2×C42 ▷ C22 ▷ C1 | |
985 conjugacy classes of subgroups.
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72210224, C2×#72211373, #72213177 |
| maximal normal subgroup of | C2×#72211373, #72213177 |
Past the SmallGroups library coverage — no SmallGroups id.