Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#72216484 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #93099 |
| commutator | C26 | C2×C42 |
| Frattini, cosocle | C2×#2846 | C23 |
| prime radical | C22×#2846 | C22 |
| LCS | G ▷ C26 ▷ C25 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C26 ◁ C22×#2846 ◁ G | |
| LECS | G ▷ C2×#2846 ▷ C25 ▷ C23 ▷ C2 ▷ C1 | |
59850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216490, C2×#72216504, C2×#72216682 |
| maximal normal subgroup of | C2×#72216490, C2×#72216504, C2×#72216682 |
Past the SmallGroups library coverage — no SmallGroups id.