Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C226 |
| direct product | C2×#72240239 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C25×D4 |
| commutator, Frattini, cosocle | C2×C4 | C28 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×#525 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Only the 443744 normal subgroups are shown; non-normal subgroups are omitted.
344 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72292698 |
| maximal normal subgroup of | C2×#72292698 |
Past the SmallGroups library coverage — no SmallGroups id.