Finite Group DatabasebetaFinite Group Databasebeta| order | 12960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D5×#13049813 |
| Fitting, socle, Hall | C34×C5 ⋊ C22×D4 |
| Sylow | C34 ⋊ C2×D4×D5 |
| Sylow | C5 ⋊ C2×#13049813 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C5×C3⋊(C3⋊(C3⋊D3)) | C24 |
| Fitting, socle, hypocenter | C34×C5 | C22×D4 |
| LCS | G ▷ C5×C3⋊(C3⋊(C3⋊D3)) ▷ C34×C5 | |
| UCS | C1 | |
3496 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 3496 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#13049813 |
| maximal normal subgroup of | AGL(1,𝔽5)×#13049813 |
Past the SmallGroups library coverage — no SmallGroups id.