Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | D8×#3025 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×#120 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| socle | C22 | C2×D4×#120 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
66872 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #72343281 |
| maximal normal subgroup of | #72343281 |
Past the SmallGroups library coverage — no SmallGroups id.