Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C11⋊C5×#534 |
| Fitting, Hall | C11×#534 ⋊ C5 |
| Sylow | C11 ⋊ C5×#534 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C11⋊C5 |
| commutator, socle, cosocle | C22×C11 | C24×C5 |
| Fitting | C11×#534 | C5 |
| hypercenter | #534 | C11⋊C5 |
| hypocenter | C11 | C5×#534 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ #534 | |
692 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#3484, #534×AGL(1,𝔽11), #72269565 |
| maximal normal subgroup of | C11⋊C5×#3484, #534×AGL(1,𝔽11), #72269565 |
Past the SmallGroups library coverage — no SmallGroups id.