Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C2×#481073 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#102 |
| commutator | C8 | C24×C8 |
| Frattini, cosocle | C4×C8 | C25 |
| socle | C22 | C22×D4⋊C8 |
| prime radical | C2×#3584 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#131 ◁ C2×C4×#131 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
7139 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72224948, C2×#72224958, C2×#72224957 |
| maximal normal subgroup of | C2×#72224948, C2×#72224958, C2×#72224957 |
| maximal quotient of | #72321655, C2×#72286692 |
Past the SmallGroups library coverage — no SmallGroups id.