Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215×C5 |
| direct product | C23×D4×C5⋊D5 |
| Fitting | C23×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C5⋊D5 |
| commutator, cosocle | C2×C52 | C26 |
| Frattini | C2 | C25×C5⋊D5 |
| Fitting | C23×C52×D4 | C2 |
| socle | C24×C52 | C23 |
| hypercenter | C23×D4 | C5⋊D5 |
| hypocenter | C52 | C24×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
42208 conjugacy classes of subgroups; only the 6107 normal subgroups are shown.
This group has 42208 conjugacy classes of subgroups — too many to draw. Only its 6107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D4×#1043, C5⋊D5×#3484, #72223249, … |
| maximal normal subgroup of | C23×D4×#1043, C5⋊D5×#3484, #72223249, … |
| maximal quotient of | C5⋊D5×#3498, C5⋊D5×#3484 |
Past the SmallGroups library coverage — no SmallGroups id.