Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C22×#133842 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #8541 |
| commutator | C22×Q8 | C24×C4 |
| Frattini, cosocle | C23×Q8 | C25 |
| prime radical | C22×#60400 | C2 |
| LCS | G ▷ C22×Q8 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C25×Q8 ◁ G | |
| LECS | G ▷ C23×Q8 ▷ C23 ▷ C2 ▷ C1 | |
149228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #72266483 |
| maximal normal subgroup of | #72266483 |
Past the SmallGroups library coverage — no SmallGroups id.