Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#72216567 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #496225 |
| commutator | C22×D4 | C24×C4 |
| Frattini, cosocle | C2×#127 | C25 |
| prime radical | C2×#6437445 | C2 |
| LCS | G ▷ C22×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C25×C4 ◁ C23×#535 ◁ G | |
| LECS | G ▷ C2×#127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
38486 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216901, C2×#72216611, #72256441, … |
| maximal normal subgroup of | C2×#72216901, C2×#72216611, #72256441, … |
Past the SmallGroups library coverage — no SmallGroups id.