Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#72216329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #213828 |
| commutator | C25 | C24×C4 |
| Frattini, cosocle | C23×D4 | C25 |
| prime radical | C2×#6499867 | C2 |
| LCS | G ▷ C25 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C24×D4 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
75540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216398, C2×#72216682, C2×#72216719 |
| maximal normal subgroup of | C2×#72216398, C2×#72216682, C2×#72216719 |
Past the SmallGroups library coverage — no SmallGroups id.