Finite Group DatabasebetaFinite Group Databasebeta| order | 2600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | C5⋊D5×#261 |
| Fitting, socle, derived, Hall | C52×C13 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×#261 |
| Sylow | C13 ⋊ C4×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C13 | C2×C4 |
| prime radical | D13×C5⋊D5 | C2 |
| cosocle | C52×D13 | C22 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#1043, C5⋊D5×AGL(1,𝔽13), D52×#261, … |
| maximal normal subgroup of | #261×#1043, C5⋊D5×AGL(1,𝔽13), D52×#261, … |
Past the SmallGroups library coverage — no SmallGroups id.