Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#130062 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #1790 |
| commutator | C2×C22⋊C4 | C23×C4 |
| Frattini, cosocle | C22×C22⋊C4 | C24 |
| prime radical | C2×#46996 | C2 |
| LCS | G ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C23×C22⋊C4 ◁ G | |
| LECS | G ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
6779 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216464, #72283992, #72284164, … |
| maximal normal subgroup of | C2×#72216464, #72283992, #72284164, … |
| maximal quotient of | #72285549, #72285835, C2×#72216452, … |
Past the SmallGroups library coverage — no SmallGroups id.