Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#72283833 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×#127 |
| commutator, Frattini, cosocle | C2×C42 | C26 |
| socle | C23 | C2×#2397 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8 ◁ C23×C4×C8 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
34360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72283979 |
| maximal normal subgroup of | C2×#72283979 |
| automorphism group of | #7331 |
Past the SmallGroups library coverage — no SmallGroups id.