Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D52×H(5,𝔽2) |
| Fitting | C52×H(5,𝔽2) ⋊ C22 |
| Sylow | C52 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D52 |
| commutator, socle, cosocle | C2×C52 | C26 |
| Fitting | C52×H(5,𝔽2) | C22 |
| hypercenter | H(5,𝔽2) | D52 |
| hypocenter | C52 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
14018 conjugacy classes of subgroups.
272 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.