Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C42 |
| direct product | C2×#72213396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #10745 |
| commutator | C22×Q8 | C22×C42 |
| Frattini, cosocle | C23×#41 | C24 |
| prime radical | C23×#535 | C22 |
| LCS | G ▷ C22×Q8 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C24×#41 ◁ G | |
| LECS | G ▷ C23×#41 ▷ C23 ▷ C2 ▷ C1 | |
34114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216901, C2×#72213457, C2×#72215603, … |
| maximal normal subgroup of | C2×#72216901, C2×#72213457, C2×#72215603, … |
| maximal quotient of | #72261736, D3×#72213396 |
Past the SmallGroups library coverage — no SmallGroups id.