Finite Group DatabasebetaFinite Group Databasebeta| order | 15600 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4×C5 |
| direct product | #1044×AGL(1,𝔽13) |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C3×C42 |
| Hall | #261×#1044 ⋊ C3 |
| Hall | C52×C13⋊C3 ⋊ C42 |
| Hall | C13⋊C3 ⋊ C4×#1044 |
| Sylow | C52 ⋊ C4×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×C4×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C13 | C3×C42 |
| prime radical | C5⋊D5×D13⋊C3 | C22 |
| cosocle | D13×C5⋊D5 | C22×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
304 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 130 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | AGL(1,𝔽13)×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.