Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C219×C4 |
| direct product | C2×#7629144 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C4 | C25 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
147669 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72268516, C2×#72279346, C2×#72327577 |
| maximal normal subgroup of | C2×#72268516, C2×#72279346, C2×#72327577 |
| maximal quotient of | C2×#72280535, #72315037, C2×#72327623, … |
Past the SmallGroups library coverage — no SmallGroups id.