Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C44 |
| direct product | C4×#110273 |
| subgroup | G/H | |
|---|---|---|
| center | C43 | #127 |
| commutator | C42 | C2×C43 |
| Frattini, cosocle | C23×C42 | C24 |
| socle | C23 | C2×#1437 |
| prime radical | C2×#3444 | C23 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C43 ◁ C22×C43 ◁ G | |
| LECS | G ▷ C23×C42 ▷ C22 ▷ C1 | |
34026 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
608 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72239526, C4×#72209725, C4×#72209990 |
| maximal normal subgroup of | #72239526 |
Past the SmallGroups library coverage — no SmallGroups id.