Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | D4×C22⋊AGL(1,𝔽11) |
| Fitting | C22×D4×C11 ⋊ C2×C5 |
| Hall | D4×C22⋊D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ D42 |
| Sylow | C11 ⋊ C5×D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×AGL(1,𝔽11) |
| commutator, socle, cosocle | C22×C11 | C24×C5 |
| Fitting | C22×D4×C11 | C2×C5 |
| hypercenter | C22×D4 | AGL(1,𝔽11) |
| hypocenter | C11 | C5×D42 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
856 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
145 conjugacy classes — view the full character table.
| maximal subgroup of | #72248978, #72248983, #72248996, … |
| maximal normal subgroup of | #72248978, #72248983, #72248996, … |
Past the SmallGroups library coverage — no SmallGroups id.