Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#72216457 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #485605 |
| commutator, Frattini, cosocle | #379 | C25 |
| LCS | G ▷ #379 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C26 ◁ C22×#379 ◁ G | |
| LECS | G ▷ #379 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
26036 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #72292088, #72292097, C2×#72216466 |
| maximal normal subgroup of | #72292088, #72292097, C2×#72216466 |
| maximal quotient of | #72292088, #72340399, #72340478 |
Past the SmallGroups library coverage — no SmallGroups id.