Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212×C4 |
| direct product | C2×#72210578 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #15258 |
| commutator, Frattini, cosocle | C26 | C25 |
| LCS | G ▷ C26 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C27 ◁ G | |
| LECS | G ▷ C26 ▷ C22 ▷ C1 | |
At least 6031 conjugacy classes of subgroups; only the 1472 normal subgroups are shown.
164 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216662, C2×#72216466, C2×#72216504, … |
| maximal normal subgroup of | C2×#72216662, C2×#72216466, C2×#72216504, … |
Past the SmallGroups library coverage — no SmallGroups id.