Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#72231264 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #152017 |
| commutator | #532 | C23×C4 |
| Frattini, cosocle | #3151 | C24 |
| prime radical | C2×#6348994 | C2 |
| LCS | G ▷ #532 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23 ◁ C23×C4 ◁ C23×C42 ◁ C2×#60801 ◁ G | |
| LECS | G ▷ #3151 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
14371 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72231265 |
| maximal normal subgroup of | C2×#72231265 |
Past the SmallGroups library coverage — no SmallGroups id.