Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C212 |
| direct product | #102×#120 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C23×D4 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C23×C4 | C25 |
| prime radical | C2×D4×#120 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C2×C4×#120 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
28643 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | #120×#442, #72306152, #72306155, … |
| maximal normal subgroup of | #120×#442, #72306152, #72306155, … |
| maximal quotient of | #102×B(4,𝔽2), #72343203, #72343932, … |
Past the SmallGroups library coverage — no SmallGroups id.