Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210 |
| direct product | C2×#72280553 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×C4×C22⋊C4 |
| commutator | C22×C4 | C23×C42 |
| Frattini, cosocle | C23×C8 | C25 |
| socle | C23 | C2×#1749 |
| prime radical | C24×D4 | M16 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×#97 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
19788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72280588 |
| maximal normal subgroup of | C2×#72280588 |
Past the SmallGroups library coverage — no SmallGroups id.