Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#13103854 |
| Fitting | C2×C52×C8 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×C4×D8 |
1394 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1394 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D8×D5⋊AGL(1,𝔽5), #72253303, #72253322 |
| maximal normal subgroup of | C2×D8×D5⋊AGL(1,𝔽5), #72253303, #72253322 |
Past the SmallGroups library coverage — no SmallGroups id.