Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#72236649 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C26 |
| socle | C23 | C22×B(4,𝔽2) |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×#41 ◁ G | |
| LECS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
61118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #72314018, C2×#72236721, C2×#72240898, … |
| maximal normal subgroup of | #72314018, C2×#72236721 |
Past the SmallGroups library coverage — no SmallGroups id.