Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#72216677 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #23802 |
| commutator | C2×C4×C8 | C24×C4 |
| Frattini, cosocle | C22×C4×C8 | C25 |
| socle | C23 | #359042 |
| prime radical | C2×#72213530 | C2 |
| LCS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ C2×#353159 ◁ G | |
| LECS | G ▷ C22×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
At least 6191 conjugacy classes of subgroups; only the 2347 normal subgroups are shown.
304 conjugacy classes. The character table is too large to display.
| maximal normal subgroup of | #72218147 |
Past the SmallGroups library coverage — no SmallGroups id.