Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C23×#87886 |
| Fitting | C25×C52 ⋊ C22 |
| Sylow | C52 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D52 |
| commutator, cosocle | C2×C52 | C26 |
| Frattini | C2 | C24×D52 |
| Fitting | C25×C52 | C22 |
| socle | C24×C52 | C23 |
| hypercenter | C25 | D52 |
| hypocenter | C52 | C24×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C24 ◁ C25 | |
26754 conjugacy classes of subgroups; only the 4100 normal subgroups are shown.
This group has 26754 conjugacy classes of subgroups — too many to draw. Only its 4100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
368 conjugacy classes. The character table is too large to display.
| maximal quotient of | #72223301 |
Past the SmallGroups library coverage — no SmallGroups id.