Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#142538 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #2021 |
| commutator, Frattini, cosocle | C22×C22⋊C4 | C24 |
| prime radical | C2×#23984 | C2 |
| LCS | G ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C23×C22⋊C4 ◁ G | |
| LECS | G ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
8259 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72233789, C2×#72233457, C2×#72260907 |
| maximal normal subgroup of | C2×#72233789, C2×#72233457 |
| maximal quotient of | #72261963, #72262103 |
Past the SmallGroups library coverage — no SmallGroups id.