Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | Q8×#1304 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#95 |
| commutator | C24 | C22×C42 |
| Frattini, prime radical, cosocle | C26 | C24 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25×Q8 ◁ G | |
| LECS | G ▷ C26 ▷ C22 ▷ C1 | |
11911 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
130 conjugacy classes — view the full character table.
| derived subgroup of | #72267720 |
| Fitting subgroup of | #72267720 |
| maximal subgroup of | #72267720 |
| maximal normal subgroup of | #72267720 |
| maximal quotient of | #72267711 |
Past the SmallGroups library coverage — no SmallGroups id.