Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#72214315 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #2094 |
| commutator | C2×C4×C8 | C23×C4 |
| Frattini, cosocle | C22×C4×C8 | C24 |
| socle | C23 | #11323 |
| prime radical | C25 | #450 |
| LCS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ C22×#1744 ◁ G | |
| LECS | G ▷ C22×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
6576 conjugacy classes of subgroups.
200 conjugacy classes — view the full character table.
| maximal subgroup of | #72214551, #72217071 |
| maximal normal subgroup of | #72214551, #72217071, C2×#72216677 |
Past the SmallGroups library coverage — no SmallGroups id.