Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#97555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #379 |
| commutator | C25 | C23×C4 |
| Frattini, cosocle | C26 | C24 |
| prime radical | C2×#35390 | C2 |
| LCS | G ▷ C25 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C27 ◁ G | |
| LECS | G ▷ C26 ▷ C23 ▷ C1 | |
15691 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 15691 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72309397, #72310558, #72310564, … |
| maximal normal subgroup of | #72309397, #72310558, #72310564, … |
Past the SmallGroups library coverage — no SmallGroups id.