Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#128008 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #342 |
| commutator | C22×C4 | C22×C42 |
| Frattini, cosocle | C23×D4 | C24 |
| socle | C23 | C2×#342 |
| prime radical | C24×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ C24×#41 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
12737 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214258, C2×#72214449, C2×#72214368, … |
| maximal normal subgroup of | C2×#72214258, C2×#72214449, C2×#72214368, … |
Past the SmallGroups library coverage — no SmallGroups id.