Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C5×C8 |
| direct product | C82×C5⋊D5 |
| Fitting | C52×C82 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | C5⋊D5 |
| commutator, hypocenter | C52 | C2×C82 |
| Frattini | C42 | C22×C5⋊D5 |
| Fitting | C52×C82 | C2 |
| socle | C22×C52 | C2×C42 |
| prime radical | C22×C5⋊D5 | C42 |
| cosocle | C42×C52 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C82 | |
1120 conjugacy classes of subgroups.
896 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C82×#1043, C5⋊D5×#1455, #72221097, … |
| maximal normal subgroup of | C82×#1043, C5⋊D5×#1455, #72221097, … |
Past the SmallGroups library coverage — no SmallGroups id.