Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C218 |
| direct product | C2×#7633646 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C42 | C24 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
54133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
256 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#72239530, #72261991, C2×#72260486 |
| maximal subgroup of | #72261931, C2×#72239530, C2×#72234084 |
| maximal normal subgroup of | #72261931, C2×#72239530, C2×#72234084 |
Past the SmallGroups library coverage — no SmallGroups id.