Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4×C5 |
| direct product | C22×C42×C5⋊D5 |
| Fitting | C22×C42×C52 ⋊ C2 |
| derived, Sylow | C52 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | C5⋊D5 |
| commutator, hypocenter | C52 | C23×C42 |
| Frattini | C22 | C24×C5⋊D5 |
| Fitting | C22×C42×C52 | C2 |
| socle | C24×C52 | C23 |
| prime radical | C24×C5⋊D5 | C22 |
| cosocle | C22×C52 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C42 | |
12000 conjugacy classes of subgroups; only the 3243 normal subgroups are shown.
This group has 12000 conjugacy classes of subgroups — too many to draw. Only its 3243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1600 |
896 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#13100501, C22×C42×#1043, C22×#13104814 |
| maximal normal subgroup of | C22×#13100501, C22×C42×#1043, C22×#13104814 |
Past the SmallGroups library coverage — no SmallGroups id.