Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#482657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#99 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C2×C4⋊C4 | C25 |
| prime radical | C2×#34963 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C22×C42 ◁ C22×C4×#41 ◁ G | |
| LECS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
8041 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72282281, #72313936, #72313950 |
| maximal normal subgroup of | C2×#72282281, #72313936, #72313950 |
Past the SmallGroups library coverage — no SmallGroups id.