Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C2×#511821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #32898 |
| commutator, Frattini, cosocle | C2×#41 | C25 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
21379 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | #72312665, C2×#72237540, C2×#72237523 |
| maximal normal subgroup of | #72312665, C2×#72237540, C2×#72237523 |
| maximal quotient of | #72279069 |
Past the SmallGroups library coverage — no SmallGroups id.