Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C245 |
| abelian | C210 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
229755605 conjugacy classes of subgroups.
1024 conjugacy classes. The character table is too large to display.
| center of | C29×D4 |
| Fitting subgroup of | #72238792, #72238793, #72257366, … |
| socle of | C29×D4 |
| maximal subgroup of | C211, C29×C4, C210×C3, … |
| maximal normal subgroup of | C211, C29×C4, C210×C3, … |
| maximal quotient of | C211, C29×C4, C210×C3, … |
| automorphism group of | #1916, #1917, #1923, … |
| outer automorphism group of | #10907, #10908, #11066, … |
Past the SmallGroups library coverage — no SmallGroups id.