Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C216 |
| direct product | C2×#72239651 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #2433 |
| commutator | C23×C4 | C24×C4 |
| Frattini, cosocle | C24×C4 | C25 |
| socle | C23 | #14715 |
| prime radical | C22×#62811 | C2 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C24×C4 ▷ C2 ▷ C1 | |
Only the 9120 normal subgroups are shown; non-normal subgroups are omitted.
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72239654 |
| maximal normal subgroup of | C2×#72239654 |
Past the SmallGroups library coverage — no SmallGroups id.