Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D52×#121 |
| Fitting | C52×#121 ⋊ C22 |
| Sylow | C52 ⋊ C22×#121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D52 |
| commutator, socle, cosocle | C22×C52 | C25 |
| Fitting | C52×#121 | C22 |
| hypercenter | #121 | D52 |
| hypocenter | C52 | C22×#121 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #121 | |
5482 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #121×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | #121×D5⋊AGL(1,𝔽5) |
| maximal quotient of | #72242560, #72242561 |
Past the SmallGroups library coverage — no SmallGroups id.