Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×#417970 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #2404 |
| commutator, Frattini, cosocle | C25 | C25 |
| prime radical | C23×H(5,𝔽2) | C22 |
| LCS | G ▷ C25 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C26 ◁ G | |
| LECS | G ▷ C25 ▷ C2 ▷ C1 | |
17685 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #72252225, #72252231, C2×#72210036 |
| maximal normal subgroup of | #72252225, #72252231, C2×#72210036 |
Past the SmallGroups library coverage — no SmallGroups id.