Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C2×#10574873 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×#120 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24×D4 ◁ G | |
| LECS | G ▷ C23 ▷ C2 ▷ C1 | |
Only the 38405 normal subgroups are shown; non-normal subgroups are omitted.
226 conjugacy classes — view the full character table.
| maximal subgroup of | #72240611, #72241100, #72251188, … |
| maximal normal subgroup of | #72240611, #72241100, #72251188, … |
| maximal quotient of | C2×#72234135, #72256562, C2×#72233689, … |
Past the SmallGroups library coverage — no SmallGroups id.