Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D52×D8 |
| Fitting | C2×C52×D8 ⋊ C22 |
| Sylow | C52 ⋊ C23×D8 |
4290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D8×D5⋊AGL(1,𝔽5), #72242561, #72242602 |
| maximal normal subgroup of | C2×D8×D5⋊AGL(1,𝔽5), #72242561, #72242602 |
Past the SmallGroups library coverage — no SmallGroups id.