Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| isoclinism | isoclinic class of #87856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4⋊#1043 |
| Fitting | C23×C4×C52 ⋊ C4 |
| Sylow | C52 ⋊ C23×C4⋊C4 |
9952 conjugacy classes of subgroups; only the 1814 normal subgroups are shown.
This group has 9952 conjugacy classes of subgroups — too many to draw. Only its 1814 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D4×#1043, #72223234, #72223296, … |
| maximal normal subgroup of | C23×D4×#1043, #72223234, #72223296, … |
| maximal quotient of | #72223253, #72223257 |
Past the SmallGroups library coverage — no SmallGroups id.